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REVIEW 3 major objections 7 minor 64 references

R-axion can drop below Planck scale and double as dark matter

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-08 07:47 UTC pith:453DEWQR

load-bearing objection Evasion of DFK bound via D_T W = 0 is clean and new; bounce action numerical prefactor is unreliable but parametric scaling holds the 3 major comments →

arxiv 2607.06375 v1 pith:453DEWQR submitted 2026-07-07 hep-th hep-ph

An Intermediate Scale R-axion \& the QCD Axion

James Unwin This is my paper
classification hep-th hep-ph
keywords R-axionQCD axionsupersymmetrydark matterstrong CP problemDine-Festuccia-Komargodski boundsupergravitymetastable vacuum
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The Dine-Festuccia-Komargodski (DFK) bound is a no-go result in supersymmetric theories: it says that if you break supersymmetry and an R-symmetry in a nearly flat (Minkowski) vacuum, the decay constant of the resulting R-axion must sit at the Planck scale. That would make the R-axion far too light and cosmologically troublesome, and would rule out identifying it with the QCD axion. This paper shows that the DFK bound can be evaded locally in an effective field theory construction. The key move is a mixed F-term and D-term uplift of the vacuum energy in which the modulus field carrying the R-axion satisfies D_T W = 0 at the minimum, meaning it sits orthogonal to the supersymmetry-breaking direction. When that condition holds, the covariant form of the DFK inequality becomes trivially satisfied (0 ≤ f_R F) and no longer forces f_R to the Planck scale. The paper then shows that two independent requirements — EFT validity (the saxion mass must lie below the EFT cutoff) and metastability of the resulting vacuum (the false vacuum must survive longer than the age of the universe) — each reintroduce a weaker lower bound: f_R ≳ √(m_{3/2} M_Pl). For TeV-scale supersymmetry, this permits f_R ~ 10^11 GeV, which is precisely the scale where a QCD axion can reproduce the observed dark matter abundance via the misalignment mechanism. If the R-symmetry has a QCD anomaly, the R-axion can serve as the QCD axion, solving the strong CP problem and providing dark matter from a symmetry already present in supersymmetric extensions of the Standard Model.

Core claim

The paper identifies a specific mechanism — the condition D_T W = 0 at a metastable minimum in a mixed F/D-term uplift — that locally disables the DFK bound's inference from the superpotential inequality 2|⟨W⟩| ≤ f_R F to the Planckian conclusion f_R ≳ M_Pl. When the modulus T containing the R-axion is arranged to be supersymmetric at the minimum (D_T W = 0), the R-Goldstone direction has zero projection onto the SUSY-breaking F-term, so the cosmological constant cancellation is handled by the uplift sector rather than forcing f_R to be large. The resulting vacuum is metastable, and demanding its lifetime exceed the age of the universe yields the relaxed bound f_R ≳ 400^{1/4} √(m_{3/2} M_Pl)

What carries the argument

The D_T W = 0 condition at a mixed F/D-term uplifted minimum, combined with a small parameter ε in the Kähler potential controlling f_R = √2 ε M_Pl at the special point s = 0

Load-bearing premise

The construction depends on a small parameter ε ≪ 1 in the Kähler potential to suppress f_R below the Planck scale, and the paper does not derive this parameter from any UV mechanism — it only speculates that approximate symmetries or UV dynamics might generate it.

What would settle it

A UV completion that either cannot generate the small Kähler parameter ε, or in which weak-gravity-type constraints forbid the required ultraweak gauge coupling g ~ m_{3/2}/M_Pl, would close the viable parameter space for an intermediate scale R-axion in this construction.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If correct, an R-symmetry already required by supersymmetric model building could simultaneously solve the strong CP problem and provide dark matter, removing the need for a separately imposed Peccei-Quinn symmetry.
  • The metastable vacuum lifetime bound f_R ≳ few × 10^11 GeV (for TeV SUSY) places the R-axion squarely in the observational window for QCD axion dark matter searches and astrophysical constraints.
  • The mixed F/D uplift structure naturally generates Dirac gaugino masses via D-term spurions, suggesting the same sector that enables small f_R also makes the R-symmetric visible sector phenomenologically viable.
  • The low EFT cutoff Λ ~ f_R²/M_Pl means Planck-suppressed R-violating operators are less suppressed than usual, but if the global R-symmetry descends from a UV gauge symmetry, instanton effects can be exponentially small as exp(-M_Pl⁴/f_R⁴).

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The construction requires a small unexplained parameter ε ≪ 1 in the Kähler potential to suppress f_R below M_Pl. If no UV mechanism generates this small parameter, the intermediate scale is not naturally selected and the model's phenomenological viability depends on an unexplained hierarchy.
  • The model generically requires an ultraweak gauge coupling g ~ m_{3/2}/M_Pl in the uplift sector, which may conflict with weak-gravity-type constraints in any quantum gravity completion, suggesting the viable parameter space is narrower than the EFT analysis alone indicates.
  • The special case r* ≈ 3 could yield an absolutely stable (rather than metastable) vacuum with f_R ~ √(m_{3/2} M_Pl), but requires tuning r* = 3 - δ with δ ~ 10^{-30}, trading one fine-tuning for another.
  • If the R-axion is identified with the QCD axion and the anomaly coefficient |N_R| ≠ 1, domain wall formation during post-inflationary symmetry breaking would be cosmologically problematic, constraining the allowed R-charge assignments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. This paper presents an effective field theory construction in which the Dine-Festuccia-Komargodski (DFK) lower bound on the R-axion decay constant, $f_R$, is evaded locally. The key mechanism is a mixed F- and D-term uplift in which the condition $D_T W = 0$ is satisfied at the minimum, so that the modulus $T$ (containing the R-axion) is absent from the supersymmetry-breaking direction. This allows $f_R$ to be parametrically below $M_{Pl}$, controlled by a small parameter $epsilon$ in the Kahler potential. The author then derives two lower bounds on $f_R$: one from EFT validity (requiring the saxion mass to be below the cutoff) and one from vacuum metastability (requiring the bounce action for tunneling to a deeper Planckian-$f_R$ vacuum to be sufficiently large). Both bounds scale as $f_R > sqrt(m_{3/2} M_{Pl})$, which for TeV-scale SUSY permits $f_R sim 10^{11}$ GeV. The paper further discusses the conditions under which this R-axion can be identified with the QCD axion, including anomaly coefficients and the mu-term generation.

Significance. The paper addresses a well-known obstruction (the DFK bound) to realizing an intermediate-scale R-axion, which is relevant for both the strong CP problem and dark matter. The construction is a proof-of-principle EFT counterexample to the folk theorem that $f_R$ must be Planckian. The derivation of the relaxed bound $f_R > sqrt(m_{3/2} M_{Pl})$ from two independent requirements (EFT validity and metastability) is a clean and notable result. The author is commendably transparent about the limitations: the need for a small unexplained parameter $epsilon$, the Planckian VEV of the uplift field, the ultraweak gauge coupling, and the need for UV completion. The phenomenological connection to the QCD axion dark matter window is clearly laid out, including the anomaly coefficient analysis and the Kim-Nilles-type mu-term generation.

major comments (3)
  1. Section 4, Eqs. (4.6)-(4.15): The metastability bound of Eq. (4.15), $f_R > 400^{1/4} sqrt(m_{3/2} M_{Pl})$, is derived from the bounce action estimate $S_4 sim (f_R^2 / (M_{Pl} m_{3/2}))^2$ using the truncated potential of Eq. (4.7). The author acknowledges that the expansion parameter $c s_b^2 / epsilon^2$ is order one at the barrier, so higher-order terms are not parametrically suppressed and the numerical prefactor is unreliable. However, the specific numerical bound of Eq. (4.15) depends precisely on these unreliable prefactors through the requirement $S_4 > 400$. The parametric scaling $S_4 sim epsilon^4$ only yields the weaker statement $f_R >> sqrt(m_{3/2} M_{Pl})$ without the $400^{1/4}$ factor. The author should clarify the status of the numerical bound: either (a) downgrade Eq. (4.15) to a parametric bound $f_R > sqrt(m_{3/2} M_{Pl})$ and note that the numerical prefactor is O
  2. Section 2, Eq. (2.12): The small parameter $epsilon$ in the Kahler potential is load-bearing for the central result, as it controls the suppression of $f_R$ below $M_{Pl}$. The author acknowledges in Section 6 that this small coefficient 'may plausibly arise from approximate symmetries or UV dynamics' but does not provide a concrete mechanism. While this is acceptable for a proof-of-principle EFT construction, the paper would be substantially strengthened by at least one explicit example (even schematic) of a UV symmetry or dynamics that naturally generates $epsilon << 1$. Without this, the construction relies on an unexplained small number, which somewhat undercuts the claim that this is more natural than the fine-tuning it replaces. This is acknowledged but could be discussed more critically.
  3. Section 3, Eqs. (3.12)-(3.13) and discussion below Eq. (3.19): The construction generically requires an ultraweak gauge coupling $g sim m_{3/2}/M_{Pl}$ and a Planckian VEV for $phi$. The author notes that $r_* approx 3$ avoids the ultraweak gauge coupling but requires an additional tuning $delta sim 10^{-30}$. The interplay between these two regimes is important for the viability of the construction. The author should clarify whether the $r_* approx 3$ special case, which avoids the weak-gravity-type concern, is the more phenomenologically relevant scenario, and if so, whether the $delta sim 10^{-30}$ tuning is qualitatively different from the CC tuning it replaces.
minor comments (7)
  1. Eq. (2.19): The EFT cutoff is defined as $Lambda^{-2} = 12c (M_{Pl}^2 / f_R^4)$, but the derivation from the kinetic terms is somewhat compressed. A brief intermediate step showing how the cross-term coefficient is extracted would improve clarity.
  2. Section 4, below Eq. (4.9): The statement 'This should be sufficient to identify the $s_b$ scaling, but it is unreliable for obtaining numerical prefactors' is important and honest. It would help to explicitly state here (rather than only implicitly) that the bound of Eq. (4.15) inherits this unreliability in its numerical coefficient.
  3. Appendix A.3, Eq. (A.37): The notation switches between $r_*$ and $r_star$ in the text surrounding this equation. Consistency would be appreciated.
  4. Section 5, Eq. (5.2): The anomaly coefficient $N_R = -3/2 R(H_u H_d)$ is stated without derivation. A brief reference to where this is calculated (cited as [9]) or a one-line sketch would help the reader.
  5. Section 5, footnote 3: This footnote contains an important correction to the interpretation of the model in [9]. It might be worth promoting part of this to the main text, as it clarifies the distinction between the R-axion and a separate accidental PQ axion in that earlier work.
  6. Eq. (4.15): The numerical evaluation $400^{1/4} sqrt(m_{3/2} M_{Pl}) approx few times 10^{11}$ GeV for $m_{3/2} = 1$ TeV should be checked. $400^{1/4} approx 4.5$, and $sqrt(10^3 times 10^{18}) = 10^{10.5}$ GeV $approx 3.2 times 10^{10}$ GeV, giving $approx 1.4 times 10^{11}$ GeV. The 'few' is reasonable but the arithmetic could be shown explicitly.
  7. References [13] and [15] appear to be from 2026 (arXiv:2603.28620 and 2607.01317). If these are correct and published, they should be fine; if preprints, dates should be verified.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive report. The referee's three major comments are well-taken. We address each in turn below and indicate revisions to be incorporated in the next version of the manuscript.

read point-by-point responses

  1. Referee: Section 4, Eqs. (4.6)-(4.15): The numerical bound of Eq. (4.15) depends on unreliable prefactors since the expansion parameter is order one at the barrier. The referee suggests either downgrading to a parametric bound or clarifying the status of the numerical prefactor.

    Authors: The referee is correct. We already acknowledge in the text (below Eq. (4.9)) that the expansion parameter cs_b^2/epsilon^2 is order one at the barrier, so higher-order terms are not parametrically suppressed and the numerical prefactor in S_4 is unreliable. However, Eq. (4.15) as currently written presents the 400^{1/4} factor without sufficient qualification, which could mislead readers into treating it as a robust numerical bound rather than an order-of-magnitude estimate. We will revise the presentation as follows. First, we will restate the bound in its parametric form f_R > sqrt(m_{3/2} M_Pl) as the primary result, emphasizing that this scaling is robust. Second, we will note that the requirement S_4 > 400 sets a numerical prefactor of order unity (specifically 400^{1/4} ≈ 4.5) but that this prefactor is not reliably computed within the truncated potential, since the barrier region has cs_b^2/epsilon^2 ~ O(1). We will present Eq. (4.15) as an illustrative estimate rather than a sharp bound, and add a sentence making explicit that the O(1) coefficient could shift by factors of a few in either direction once higher-order terms in the Kähler potential are included. The phenomenological conclusion — that TeV-scale SUSY permits f_R ~ 10^{11} GeV — is unaffected, since it depends only on the parametric scaling. revision: yes

  2. Referee: Section 2, Eq. (2.12): The small parameter epsilon is load-bearing but unexplained. The paper would be strengthened by at least one explicit example of a UV symmetry or dynamics generating epsilon << 1.

    Authors: We agree that providing a concrete UV mechanism for epsilon << 1 would strengthen the paper. However, we have not been able to identify a fully convincing and explicit mechanism that generates this small parameter in a controlled way within a UV completion. This is an honest limitation of the proof-of-principle construction. In the revised version, we will expand the discussion in Section 6 to be more critical about this point. Specifically, we will: (i) note more explicitly that the smallness of epsilon is an unexplained input at the EFT level, and that the construction replaces one fine-tuning (the cosmological constant) with a small parameter, which is a trade rather than a full resolution; (ii) discuss in somewhat more detail the analogy with shift-symmetric Kähler potentials in supergravity inflation models (refs. [48,49]), where small coefficients arise after symmetry breaking, and note that a similar mechanism could in principle generate epsilon if the shift symmetry of T is only approximate; (iii) acknowledge that without a concrete realization, the naturalness of epsilon << 1 remains an open question that we flag for future work. We believe a fully worked UV example is beyond the scope of this proof-of-principle paper, but the referee is right that the discussion should be more candid. revision: partial

  3. Referee: Section 3, Eqs. (3.12)-(3.13) and discussion below Eq. (3.19): Clarify whether the r* ≈ 3 special case is more phenomenologically relevant, and whether the delta ~ 10^{-30} tuning is qualitatively different from the CC tuning it replaces.

    Authors: The referee raises an important point about the interplay between the two regimes. We will add a clarifying discussion addressing both questions. Regarding phenomenological relevance: the r* ≈ 3 case is in some sense more attractive because it avoids the ultraweak gauge coupling g ~ m_{3/2}/M_Pl, which may be in tension with weak-gravity-type constraints in a UV completion. However, as we note in Appendix A.4, the r* ≈ 3 case also changes the character of the metastability analysis — the D-term contribution to the vacuum energy becomes parametrically small, and the trajectory toward the Planckian-f_R region is modified. In particular, the trial trajectory used in Appendix A.3 to demonstrate the existence of a deeper vacuum is no longer useful, and s = 0 may in fact be the global minimum (though we do not prove this). If s = 0 is the global minimum, the metastability bound of Section 4 would not apply, which would be favorable. However, this conclusion is sensitive to higher-order Kähler corrections in the uplift sector since r is large. Regarding the delta ~ 10^{-30} tuning: we agree this requires comment. This tuning is qualitatively different from the cosmological constant tuning in one respect — it is a tuning of a parameter (r*) rather than a cancellation between two unrelated quantities — but it is quantitatively comparable in precision. We will state explicitly that the r* ≈ 3 scenario trades the ultraweak gauge coupling problem for a tuning problem of comparable severity to the CC tuning, and that neither regime is fully satisfactory without a dynamical mechanism. We will note that a dynamical mechanism pushing r* near 3 could conceivably exist but is not explored here. This honest assessment will be added to Section 3 and Appendix A.4. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation chain is self-contained with one minor non-load-bearing self-citation.

full rationale

The paper's central derivation chain is self-contained. The DFK bound evasion follows from direct computation: the Kähler potential (eq. 2.12) and superpotential (eq. 2.11) yield D_T W = 0 at s = 0 (eq. 2.25), which reduces the covariant DFK inequality to the trivial 0 ≤ f_R F (eq. 2.10). The small decay constant f_R(0) = √2 ε M_Pl (eq. 2.17) follows directly from K_{T T̄} at s = 0, with ε as an explicit input parameter — not a fitted constant renamed as a prediction. The EFT validity bound (eq. 2.20) derives from requiring m_σ < Λ where both quantities are independently computed from the model. The metastability bound (eq. 4.15) follows from a bounce action estimate (eq. 4.14) built from the model's own potential, and the paper transparently acknowledges the truncated expansion's limitations for numerical prefactors. The one self-citation [9] (Unwin & Yildirim) is used for the anomaly coefficient N_R (eq. 5.2) and R-charge assignments — supplementary phenomenological context, not the load-bearing argument for DFK evasion. The paper even flags that the interpretation in [9] needs refinement (footnote 3). No step reduces to its inputs by construction, no parameter is fitted and then 'predicted,' and no uniqueness theorem is invoked to forbid alternatives. Score 1 reflects the minor self-citation that does not undermine the independent content of the central derivation.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 2 invented entities

The model introduces a small parameter $O(1)$ and an uplift sector with a Planckian VEV. The axioms rely on EFT validity and metastability, which are checked within the paper. The invented entities are standard in EFT model building but lack independent UV evidence.

free parameters (3)
  • epsilon = 1
    Small parameter in the Kähler potential (eq. 2.12) controlling the suppression of $f_R$ below $M_{Pl}$.
  • c = 1
    Coefficient of the quartic saxion term in the Kähler potential (eq. 2.12), assumed $O(1)$.
  • r_star = 1 < r_star < 3
    Labels the chosen stationary point of the uplift sector (eq. 3.3), not derived but fixed by unspecified UV dynamics.
axioms (3)
  • domain assumption Validity of effective field theory with a cutoff $O(m_{3/2} M_{Pl})^{1/2}$
    The EFT validity bound (eq. 2.20) assumes the saxion mass is below the cutoff scale $O(1)$, which is derived from the Kähler potential structure.
  • domain assumption Metastability of the small-$f_R$ vacuum
    The phenomenological viability relies on the vacuum lifetime exceeding the age of the universe, which is checked via a bounce action calculation (Section 4).
  • domain assumption Existence of a UV completion for the uplift sector
    The effective FI parameter and Planckian VEV of $O(1)$ require a UV completion, which is assumed to exist but not constructed (Section 6).
invented entities (2)
  • Uplift field phi no independent evidence
    purpose: Chiral field with R-charge zero and charge +1 under a gauged U(1)_X, providing the mixed F- and D-term uplift.
    Introduced in the EFT to stabilize the vacuum; its UV dynamics are not specified.
  • Gauged U(1)_X no independent evidence
    purpose: Gauge symmetry under which the uplift field phi is charged, providing the D-term for the uplift.
    Postulated as part of the effective construction; requires UV completion.

pith-pipeline@v1.1.0-glm · 23213 in / 2533 out tokens · 329530 ms · 2026-07-08T07:47:23.593174+00:00 · methodology

0 comments
read the original abstract

An intermediate scale R-axion faces an immediate obstruction from the Dine-Festuccia-Komargodski (DFK) bound on the superpotential, $2|\langle W\rangle|\leq f_R F$, since for a nearly Minkowski vacuum it typically follows that $f_R\gtrsim M_{\rm Pl}$. We show that this lower bound on $f_R$ can be relaxed in an effective construction with the scalar potential tuned near zero via a mixed $F$- and $D$-term uplift, leading to a metastable vacuum in which the usual Planckian-$f_R$ inference from the DFK argument is avoided locally. Validity of the effective field theory and metastability of the small $f_R$ vacuum generically both imply a relaxed bound: $ f_R \gtrsim \sqrt{m_{3/2}M_{\rm Pl}} $. We also highlight that if the R-symmetry has a QCD anomaly, this potentially permits the R-axion to play the role of the QCD axion. TeV-scale supersymmetry permits $f_R\sim10^{11}$ GeV, this not only evades certain astrophysical and cosmological axion constraints, but notably lies in the window for which the observed dark matter abundance can be reproduced by the R-axion via the misalignment mechanism.

discussion (0)

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Reference graph

Works this paper leans on

64 extracted references · 64 canonical work pages · 38 internal anchors

  1. [1]

    R. J. Crewther, P. Di Vecchia, G. Veneziano and E. Witten,Chiral Estimate of the Electric Dipole Moment of the Neutron in Quantum Chromodynamics,Phys. Lett. B88, 123 (1979) [erratum: Phys. Lett. B91, 487 (1980)]

    work page 1979

  2. [2]

    J. M. Pendlebury,et al. Revised experimental upper limit on the electric dipole moment of the neutron,Phys. Rev. D92, no.9, 092003 (2015) [1509.04411]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  3. [3]

    R. D. Peccei and H. R. Quinn,CP Conservation in the Presence of Instantons,Phys. Rev. Lett.38, 1440-1443 (1977)

    work page 1977

  4. [4]

    R. D. Peccei and H. R. Quinn,Constraints Imposed by CP Conservation in the Presence of Instantons,Phys. Rev. D16, 1791-1797 (1977)

    work page 1977

  5. [5]

    A. R. Zhitnitsky,On Possible Suppression of the Axion Hadron Interactions. (In Russian), Sov. J. Nucl. Phys.31, 260 (1980)

    work page 1980

  6. [6]

    M. Dine, W. Fischler and M. Srednicki,A Simple Solution to the Strong CP Problem with a Harmless Axion,Phys. Lett. B104, 199-202 (1981)

    work page 1981

  7. [7]

    Kim,Weak Interaction Singlet and Strong CP Invariance,Phys

    J. Kim,Weak Interaction Singlet and Strong CP Invariance,Phys. Rev. Lett.43(1979) 103

    work page 1979

  8. [8]

    M. A. Shifman, A. I. Vainshtein and V. I. Zakharov,Can Confinement Ensure Natural CP Invariance of Strong Interactions?,Nucl. Phys. B166(1980) 493

    work page 1980

  9. [9]

    Unwin and T

    J. Unwin and T. Yildirim,A QCD R-axion,Phys. Rev. D111, no.1, 1 (2025) [2407.17557]

    work page arXiv 2025

  10. [10]

    Claudson, L

    M. Claudson, L. J. Hall and I. Hinchliffe,Tuning the cosmological constant inN= 1 supergravity with an R-symmetry,Phys. Lett. B130(1983), 260-264

    work page 1983

  11. [11]

    M. Dine, G. Festuccia and Z. Komargodski,A Bound on the Superpotential,JHEP03 (2010), 011 [0910.2527]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  12. [12]

    G. R. Dvali,Removing the cosmological bound on the axion scale,[hep-ph/9505253]

    work page internal anchor Pith review Pith/arXiv arXiv

  13. [13]

    Dvali, S

    G. Dvali, S. Fitz and L. Komisel,Removing the Cosmological Bound on the Axion Scale via Confinement During Inflation,[2603.28620]

    work page arXiv

  14. [14]

    String Axiverse

    A. Arvanitaki,et al. String Axiverse,Phys. Rev. D81, 123530 (2010) [0905.4720]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  15. [15]

    O. Ning, B. R. Safdi and C. Welch,No Evidence for Superradiant Axions in LIGO-Virgo-KAGRA GWTC-5 Binary Black Hole Spins,[2607.01317]

    work page internal anchor Pith review Pith/arXiv arXiv

  16. [16]

    Wess and J

    J. Wess and J. Bagger,Supersymmetry and Supergravity,Princeton University Press

    work page

  17. [17]

    G. R. Dvali and A. Pomarol,Supersymmetry breaking with vanishing F terms in supergravity theories,Phys. Lett. B410(1997), 160-166 [hep-ph/9706429]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  18. [18]

    R-symmetric Axion/Natural Inflation in Supergravity via Deformed Moduli Dynamics

    K. Harigaya, M. Ibe and T. Yanagida,R-symmetric Axion/Natural Inflation in Supergravity via Deformed Moduli Dynamics,Phys. Lett. B739, 352 (2014) [1409.0330]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  19. [19]

    Gauged R-symmetry and de Sitter vacua in supergravity and string theory

    I. Antoniadis and R. Knoops,Gauge R-symmetry and de Sitter vacua in supergravity and string theory,Nucl. Phys. B886, 43-62 (2014) [1403.1534]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  20. [20]

    Fayet and J

    P. Fayet and J. Iliopoulos,Spontaneously Broken Supergauge Symmetries and Goldstone Spinors,Phys. Lett. B51, 461-464 (1974)

    work page 1974

  21. [21]

    Fayet-Iliopoulos terms in supergravity without gauged R-symmetry

    N. Cribiori, F. Farakos, M. Tournoy and A. van Proeyen,Fayet-Iliopoulos terms in supergravity without gauged R-symmetry,JHEP04, 032 (2018) [1712.08601]. – 22 –

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  22. [22]

    Anomaly Cancellation in Supergravity with Fayet-Iliopoulos Couplings

    H. Elvang, D. Z. Freedman and B. Kors,Anomaly cancellation in supergravity with Fayet-Iliopoulos couplings,JHEP11, 068 (2006) [hep-th/0606012]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  23. [23]

    Fayet-Iliopoulos Terms in Supergravity and Cosmology

    P. Binetruy, G. Dvali, R. Kallosh and A. Van Proeyen,Fayet-Iliopoulos terms in supergravity and cosmology,Class. Quant. Grav.21, 3137-3170 (2004) [hep-th/0402046]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  24. [24]

    K. S. Stelle and P. C. West,Relation Between Vector and Scalar Multiplets and Gauge Invariance in Supergravity,Nucl. Phys. B145, 175-188 (1978)

    work page 1978

  25. [25]

    D. Z. Freedman,Supergravity with Axial Gauge Invariance,Phys. Rev. D15, 1173 (1977)

    work page 1977

  26. [26]

    Barbieri, S

    R. Barbieri, S. Ferrara, D. V. Nanopoulos and K. S. Stelle,Supergravity, R Invariance and Spontaneous Supersymmetry Breaking,Phys. Lett. B113, 219-222 (1982)

    work page 1982

  27. [27]

    Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity

    Z. Komargodski and N. Seiberg,Comments on the Fayet-Iliopoulos Term in Field Theory and Supergravity,JHEP06, 007 (2009) [0904.1159]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  28. [28]

    T. T. Dumitrescu, Z. Komargodski and M. Sudano,Global Symmetries and D-Terms in Supersymmetric Field Theories,JHEP11, 052 (2010) [1007.5352]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  29. [29]

    G. R. Dvali and A. Pomarol,Anomalous U(1) as a mediator of supersymmetry breaking, Phys. Rev. Lett.77, 3728-3731 (1996) [hep-ph/9607383]

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  30. [30]

    Dynamical supersymmetry breaking in models with a Green-Schwarz mechanism

    N. Arkani-Hamed, M. Dine and S. Martin,Dynamical supersymmetry breaking in models with a Green-Schwarz mechanism,Phys. Lett. B431, 329-338 (1998) [hep-ph/9803432]

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  31. [31]

    The String Landscape, Black Holes and Gravity as the Weakest Force

    N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa,The String landscape, black holes and gravity as the weakest force,JHEP06, 060 (2007) [hep-th/0601001]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  32. [32]

    K. A. Intriligator, N. Seiberg and D. Shih,Dynamical SUSY breaking in meta-stable vacua, JHEP04, 021 (2006) [hep-th/0602239]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  33. [33]

    K. R. Dienes and B. Thomas,Building a Nest at Tree Level: Classical Metastability and Non-Trivial Vacuum Structure in Supersymmetric Field Theories,Phys. Rev. D78, 106011 (2008) [0806.3364]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  34. [34]

    F. C. Adams,General solutions for tunneling of scalar fields with quartic potentials,Phys. Rev. D48, 2800-2805 (1993) [hep-ph/9302321]

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  35. [35]

    M. J. Duncan and L. G. Jensen,Exact tunneling solutions in scalar field theory,Phys. Lett. B291, 109-114 (1992)

    work page 1992

  36. [36]

    S. R. Coleman,The Fate of the False Vacuum. 1. Semiclassical Theory,Phys. Rev. D15, 2929-2936 (1977) [erratum: Phys. Rev. D16, 1248 (1977)]

    work page 1977

  37. [37]

    C. G. Callan, Jr. and S. R. Coleman,The Fate of the False Vacuum. 2. First Quantum Corrections,Phys. Rev. D16, 1762-1768 (1977)

    work page 1977

  38. [38]

    S. R. Coleman and F. De Luccia,Gravitational Effects on and of Vacuum Decay,Phys. Rev. D21, 3305 (1980)

    work page 1980

  39. [39]

    Srednicki,Axion Couplings to Matter

    M. Srednicki,Axion Couplings to Matter. 1. CP Conserving Parts,Nucl. Phys. B260, 689-700 (1985)

    work page 1985

  40. [40]

    Preskill, M

    J. Preskill, M. B. Wise and F. Wilczek,Cosmology of the Invisible Axion,Phys. Lett. B120, 127-132 (1983)

    work page 1983

  41. [41]

    Sikivie,Of Axions, Domain Walls and the Early Universe,Phys.Rev.Lett.48, 1156 (1982)

    P. Sikivie,Of Axions, Domain Walls and the Early Universe,Phys.Rev.Lett.48, 1156 (1982)

    work page 1982

  42. [42]

    J. E. Kim and H. P. Nilles,Symmetry principles toward solutions of the mu problem,Mod. Phys. Lett. A9, 3575-3584 (1994) [hep-ph/9406296]. – 23 –

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  43. [43]

    Fayet,Fermi-Bose Hypersymmetry,Nucl

    P. Fayet,Fermi-Bose Hypersymmetry,Nucl. Phys. B113, 135 (1976)

    work page 1976

  44. [44]

    Hall and L

    L. Hall and L. Randall,U(1)-R-symmetric supersymmetry,Nucl. Phys. B352, 289 (1991)

    work page 1991

  45. [45]

    P. J. Fox, A. E. Nelson and N. Weiner,Dirac gaugino masses and supersoft supersymmetry breaking,JHEP08, 035 (2002) [hep-ph/0206096]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  46. [46]

    G. D. Kribs, E. Poppitz and N. Weiner,Flavor in supersymmetry with an extended R-symmetry,Phys. Rev. D78, 055010 (2008) [0712.2039]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  47. [47]

    R-symmetric High Scale Supersymmetry

    J. Unwin,R-symmetric High Scale Supersymmetry,Phys. Rev. D86, 095002 (2012) [1210.4936]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  48. [48]

    Shift Symmetry and Inflation in Supergravity

    P. Brax and J. Martin,Shift symmetry and inflation in supergravity,Phys. Rev. D72, 023518 (2005) [hep-th/0504168]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  49. [49]

    SUGRA Hybrid Inflation with Shift Symmetry

    S. Antusch, K. Dutta and P. M. Kostka,SUGRA Hybrid Inflation with Shift Symmetry, Phys. Lett. B677, 221-225 (2009) [0902.2934]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  50. [50]

    Symmetries and Strings in Field Theory and Gravity

    T. Banks and N. Seiberg,Symmetries and Strings in Field Theory and Gravity,Phys. Rev. D83(2011) 084019 [1011.5120]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  51. [51]

    Symmetries in quantum field theory and quantum gravity

    D. Harlow and H. Ooguri,Symmetries in quantum field theory and quantum gravity, Commun. Math. Phys.383, no.3, 1669-1804 (2021). [1810.05338]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  52. [52]

    H. M. Georgi, L. J. Hall and M. B. Wise,Grand Unified Models With an Automatic PQ Symmetry,Nucl. Phys. B192(1981) 409

    work page 1981

  53. [53]

    Planck-Scale Physics and the Peccei-Quinn Mechanism

    M. Kamionkowski and J. March-Russell,Planck-scale physics and the PQ mechanism,Phys. Lett. B282(1992) 137 [hep-th/9202003]

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  54. [54]

    Solutions to the strong CP problem in a world with gravity

    R. Holman,et al.,Solutions to the strong CP problem in a world with gravity,Phys. Lett. B 282(1992) 132 [hep-ph/9203206]

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  55. [55]

    Barr and D

    S. Barr and D. Seckel,Planck-scale corrections to axion models,Phys. Rev. D46(1992) 539

    work page 1992

  56. [56]

    B. A. Dobrescu,The Strong CP problem versus Planck scale physics,Phys. Rev. D55(1997) 5826 [hep-ph/9609221]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  57. [57]

    GRAVITY AND GLOBAL SYMMETRIES

    R. Kallosh, A. D. Linde, D. A. Linde and L. Susskind,Gravity and global symmetries,Phys. Rev. D52, 912-935 (1995) [hep-th/9502069]

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  58. [58]

    The String Landscape and the Swampland

    C. Vafa,The String landscape and the swampland,[hep-th/0509212]

    work page internal anchor Pith review Pith/arXiv arXiv

  59. [59]

    Evidence for a Lattice Weak Gravity Conjecture

    B. Heidenreich, M. Reece and T. Rudelius,Evidence for a sublattice weak gravity conjecture, JHEP08, 025 (2017) [1606.08437]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  60. [60]

    The UV Fate of Anomalous $U(1)$s and the Swampland

    N. Craig, I. Garcia Garcia and G. D. Kribs,The UV fate of anomalous U(1)s and the Swampland,JHEP11, 063 (2020) [1912.10054]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  61. [61]

    T. Daus, A. Hebecker, S. Leonhardt and J. March-Russell,Towards a Swampland Global Symmetry Conjecture using weak gravity,Nucl. Phys. B960, 115167 (2020) [2002.02456]

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  62. [62]

    The R-axion and non-Gaussianity

    K. Nakayama and F. Takahashi,The R-axion and non-Gaussianity,Phys. Lett. B679, 436-439 (2009) [0907.0834]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  63. [63]

    A. E. Nelson and N. Seiberg,R-symmetry breaking versus supersymmetry breaking,Nucl. Phys. B416, 46-62 (1994) [hep-ph/9309299]

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  64. [64]

    The R Axion From Dynamical Supersymmetry Breaking

    J. Bagger, E. Poppitz and L. Randall,The R axion from dynamical supersymmetry breaking, Nucl. Phys. B426, 3-18 (1994) [hep-ph/9405345]. – 24 –

    work page internal anchor Pith review Pith/arXiv arXiv 1994