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Fermionic p-form gauge theory in AdS_d has a gauge-independent effective action given by a ratio of Dirac-type functional determinants.

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The BV quantization of the reducible fermionic p-form gauge theory in AdS_d gives Z(p) as a product over functional determinants of Dirac-like operators with degree-dependent masses.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A solid, careful BV derivation of the fermionic p-form determinant formula in AdS_d; the two-gauge consistency check is real evidence, but the unproved projector identity (4.23) makes the general-p result conditional. the 3 major comments →

arxiv 2509.01863 v1 pith:3UO7E7JI submitted 2025-09-02 hep-th

Covariant quantization of totally antisymmetric tensor-spinor field in $AdS_d$

A.O. Barvinsky , I.L. Buchbinder , V.A. Krykhtin , D.V. Nesterov This is my paper
classification hep-th
keywords fermionic p-formantisymmetric tensor-spinorAdS spaceBatalin-Vilkovisky quantizationreducible gauge theoryfunctional determinantseffective actiongauge independence
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 reading

This paper works out the covariant quantum theory of a totally antisymmetric tensor-spinor (fermionic p-form) field in d-dimensional anti-de Sitter space. Because the gauge transformations are reducible—their generators have zero modes at p−1 successive levels—the standard Faddeev–Popov rule does not apply. The authors use the Batalin–Vilkovisky field-antifield method with two different admissible covariant gauges and obtain the same reduced action in both. The result expresses the quantum effective action as a product of functional determinants of Dirac-like operators acting on irreducible gamma-components of the fields, with degree-dependent masses and explicit powers. If correct, this gives a concrete, gauge-independent handle on the quantum dynamics of a class of exotic supergravity-related fields.

Core claim

The central claim is Eq. (4.60)–(4.61): the generating functional of the fermionic p-form theory in AdS_d equals a ratio of products of functional determinants, Z(p) = ∏_{n=0}^{[p/2]} (∆_{p−2n})^{2n+1} / ∏_{m=0}^{[(p−1)/2]} (∆_{p−1−2m})^{−2m−2}, where ∆_s = Det(/∇ ∓ (i/2)√r0 (d−2s)) on irreducible spinor-form fields of degree s. The same expression arises from minimal-rank and full-rank algebraic gauge fixings, after reduction to the leading-parity components of the original fields, minimal ghosts, and antighosts. This confirms a conjecture about the general structure of the effective action made in an earlier work.

What carries the argument

The machinery is the algebraic decomposition of a spinor-valued r-form into gamma-irreducible pieces of degrees s, implemented by projectors P_s (Eq. 4.22–4.25). The leading-parity projector P_▼ keeps only components of degrees r, r−2, r−4, …, and these are exactly the fields surviving on the reduction surface. On each surviving component acts the massive Dirac operator /∇_s = /∇ ∓ (i/2)√r0 (d−2s), whose mass coefficient is fixed by the degree of the component; functional integration over these components produces the determinants ∆_s. The BV triangular gauge-fixing chains organize the step-by-step reduction in both gauges.

Load-bearing premise

The whole determinant product rests on an unproved algebraic lemma: that the closed-form projectors in Eq. (4.23) genuinely split every spinor-form into gamma-irreducible pieces with the stated ranks.

What would settle it

Take the smallest nontrivial case, d = 7, p = 3, and compute the projector completeness and rank identities (4.23)–(4.25) explicitly with gamma matrices; if the ranks mismatch or if direct Gaussian integration of the gauge-fixed action fails to produce Z(3) = ∆3 ∆1^3 / (∆2^2 ∆0^4), the central claim collapses.

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

If this is right

  • The complete one-loop effective action of the fermionic p-form theory is fixed by the determinant ratio (4.61) for every p and d with 2p < d.
  • The mass spectrum of the reduced theory is determined solely by the degree s of each irreducible component through the operator /∇_s.
  • Both minimal-rank and full-rank covariant gauges reduce to the same physical space, so the determinant ratio is gauge-independent.
  • For p = 3 the general formula reproduces Z(3) = ∆3 ∆1^3 / (∆2^2 ∆0^4), which can be checked by direct integration.
  • The calculation provides a template for quantizing other reducible gauge theories with multiple stages of linearly dependent generators.

Where Pith is reading between the lines

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

  • The ratio form suggests possible cancellations between numerator and denominator towers; for many d and p the effective action may collapse to a much shorter product once the determinants are evaluated explicitly.
  • The same leading-parity reduction logic likely applies to bosonic antisymmetric p-form analogues, where the role of gamma-projectors is played by Hodge-type decompositions; a direct comparison would test whether the gauge-independence mechanism generalizes.
  • If the classically dual fermionic (d−p−2)-form model exists in AdS_d, its BV reduction should produce the same determinant ratio, providing a quantum-level test of the classical duality.
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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 / 5 minor

Summary. The paper applies the Batalin-Vilkovisky (BV) formalism to quantize a free totally antisymmetric tensor-spinor field (fermionic p-form) in AdS_d, a theory with (p-1)-stage reducible gauge symmetry. It constructs the non-minimal BV action, introduces two covariant gauge fermions (minimal-rank and full-rank algebraic gauges), decomposes all fields into gamma-irreducible components, reduces the gauge-fixed action, and obtains the generating functional as a ratio of determinants of massive Dirac operators, Eqs. (4.60)-(4.61). The p=3 case is worked out explicitly and the authors claim both gauges lead to the same reduced action and the same partition function.

Significance. If the central algebraic lemma were established, this would be a valuable explicit example of BV quantization of a higher-stage reducible gauge theory with a closed-form effective action, and it would confirm the conjectured structure in [33]. The paper is technically ambitious and contains many explicit computations: the BV structure, the component reduction, and the determinant multiplicities are given in detail, with no fitted parameters. Its main defect is that the load-bearing projector identity is asserted rather than proved, and the internal cross-checks do not independently test that identity.

major comments (3)
  1. [§4.3, Eq. (4.23)] The closed-form projector P_s is stated without derivation or reference. This projector controls the decomposition (4.19), the rank and completeness properties (4.25), the mass coefficients in (4.20), (4.28), and (4.41), and ultimately the determinant multiplicities in Fig. 4 and Eq. (4.60). Both the minimal-rank and full-rank reductions use the same P_s, so their agreement does not test the normalization or combinatorics of (4.23). The p=3 check uses the same decomposition, and the benchmark [33] is the authors' own conjecture. A proof (or a precise citation) of (4.23) and of the rank identities (4.25) is necessary for the central claim.
  2. [§3.3.3] The text contains a dangling reference: 'We summarized the gauge-fixed action for p=3 case in Appendix??, see (??).' This marks an omitted derivation of the full-rank p=3 auxiliary action. Although the final reduced action (3.47) is stated, the missing passage is the only place where the full-rank p=3 reduction is verified. The reference should be restored or the missing derivation supplied; as it stands, the gauge-independence claim for the worked example is not fully supported.
  3. [§4.5, Eqs. (4.47)–(4.51)] The full-rank reduction is described through asserted 'crucial properties' and the statement that the third property 'can be proved by induction'. This induction is not given. Since this reduction produces the physical-space result (4.52) and the reduced action (4.54), the correctness of the determinant formula depends on it. Please provide a complete proof or a clear statement of the induction, and fix the notation in (4.48) where the alignment markers make the displayed equation difficult to parse.
minor comments (5)
  1. [§3.4, footnote 24] 'whereas that of degrees r-2n-1 as leading-parity ones' should presumably read 'subleading-parity ones'.
  2. [§4.6, Eq. (4.57)] The sentence defining the coefficients refers to 'c^{r-2n}_r, (4.57), (4.42)' while (4.57) is the equation being introduced; the cross-reference needs correction.
  3. [§4.3] The sentence 'For mostly presentational reasons we keep the coefficients ¯α^s_r unspecified' is followed by the explicit choice (4.17). Please clarify that (4.17) is the convention used in the final results.
  4. [§4.4, Eq. (4.35)] The displayed equation contains unexplained '::::' alignment markers that make it hard to read; these should be cleaned up.
  5. [General] The comparison with [33] should explicitly state that it is a previous work by the same authors and therefore is not an independent check of Eq. (4.60).

Circularity Check

0 steps flagged

No significant circularity: the determinant ratio is derived from BV axioms and explicit gauge fixings; the only same-author citation ([33]) is used as a confirmatory benchmark, not as a premise.

full rationale

The central result Z(p) in (4.60)-(4.61) is obtained by (i) taking the fermionic p-form action from [14] with the mass fixed by the AdS nilpotence condition, (ii) constructing the BV master action from the standard abelian reducible-gauge ansatz in Appendix A, (iii) choosing two explicit gauge fermions, and (iv) reducing to irreducible components and integrating Gaussian blocks. No equation defining the target is inserted as an input; there are no fitted parameters and no benchmark values used in the derivation. The references to [33] ('fits the general result predicted in [33]' at (3.51) and 'confirms a conjecture... put forward in [33]' after (4.61)) are same-author citations, but they are confirmatory rather than load-bearing: eliminating them would not change the derivation. The undemonstrated closed form of the projectors P_s in (4.23) and the asserted rank/completeness properties in (4.25) are proof gaps and a genuine correctness risk (both gauges share this algebraic input, so the two-gauge agreement does not test it), but this is not circularity: the lemma does not assume the final determinant formula. Likewise the dangling 'Appendix??' in Sec. 3.3.3 marks an omission, not a circular step. The self-citation is minor and the central derivation has independent content, so the circularity score is low.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

No numerical constants are fitted to data; p and d are arbitrary integers with 2p < d, and m0 is fixed by the AdS curvature through the nilpotence condition. The only non-external benchmark cited for the final determinant structure is the authors' own conjecture in [33]. No new physical particles, forces, dimensions or conserved quantities are introduced; BV ghosts and Lagrange multipliers are formal quantization artifacts.

axioms (4)
  • standard math Batalin-Vilkovisky formalism: the master action (A.13) with ghost and auxiliary sectors satisfies the master equation, and delta-function gauge fixing (A.18)-(A.23) yields a nondegenerate gauge-fixed action under suitable rank conditions.
    Invoked throughout the paper. The formalism is reviewed in Appendix A and cited to [28, 29, 31, 32], but the general BV construction itself is not rederived.
  • domain assumption The nilpotence condition D_mu D^mu f = 0 for m0 = +/- (1/2) sqrt(r0) in AdS space, Eq. (2.15), gives rise to the (p-1)-stage reducible gauge structure (2.16).
    Taken from the defining model in reference [14]. This is the property that makes the theory reducible; if it fails, the whole gauge tower on which the quantization is built does not exist.
  • standard math Completeness of the gamma-irreducible decomposition (4.16), (4.19) and the explicit projector formula (4.23) with the stated ranks.
    Load-bearing for all component decompositions, determinant masses and normalizations. The paper states the projector formula in Section 4.3 without proof.
  • domain assumption The AdS background is maximally symmetric with curvature parameter r0, and the theory is restricted to 2p < d so that the (2p+1)-gamma term and the irreducibility decomposition are nontrivial.
    The model from [14] is consistently defined only on AdS under this condition. The paper quantizes only this background and does not address arbitrary curved spacetime.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Covariant quantization of totally antisymmetric tensor-spinor field in $AdS_d$." pith.science (2026). https://pith.science/paper/3UO7E7JI

@misc{pith2026250901863,
  author       = {Pith},
  title        = {Pith review of: Covariant quantization of totally antisymmetric tensor-spinor field in $AdS_d$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3UO7E7JI}},
  note         = {Machine review of arXiv:2509.01863}
}
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abstract

We develop the quantization of a recently proposed model describing a totally antisymmetric rank-$p$ tensor-spinor field (a fermionic $p$-form theory) in $d$-dimensional anti-de Sitter (AdS) space. The model provides a new nontrivial example of a reducible gauge theory, in which gauge transformations are linearly dependent and the degree of reducibility increases with $p$. It is well known that in such cases the standard Faddeev-Popov-DeWitt prescription for the generating functional is not applicable. We quantize the fermionic $p$-form theory using the general Batalin-Vilkovisky (BV) formalism, employing two distinct gauge fermions associated with gauge-fixing functions of different admissible ranks, confirming the independence from the gauge choice. As a result, we obtain the quantum effective action in terms of a sequence of functional determinants corresponding to specific Dirac-like operators on AdS space.

Figures

Figures reproduced from arXiv: 2509.01863 by A.O. Barvinsky, D.V. Nesterov, I.L. Buchbinder, V.A. Krykhtin.

Figure 1
Figure 1. Figure 1: Triangular diagram for fermionic 3-form model With each down-left edge (line) between vertices with ghosts of degrees 𝑟 − 1 and 𝑟 one associates gauge-fixing operators16 𝑋𝜇[𝑟]𝜈[𝑟+1] , 𝑋¯ 𝜇[𝑟]𝜈[𝑟+1] . The gauge fermion (3.10) is the sum over terms, in which these gauge-fixing matrices couple ghost fields 𝒞𝜇[𝑟] , 𝒞¯ 𝜇[𝑟] and 𝒞𝜇[𝑟+1] , 𝒞¯ 𝜇[𝑟+1] from the incident vertices into combinations 𝒞¯𝑋 𝒞 and 𝒞¯𝑋¯ 𝒞 by… view at source ↗
Figure 2
Figure 2. Figure 2: Triangular diagram for fermionic 𝑝-form model At each vertex, Dirac-conjugated partners 𝜓, ¯ 𝒞¯, ℬ of the depicted fields are assumed. The degree 𝑟 of a field corresponds to its level as 𝑟 = 𝑝 − 𝑙. The gauge fermion (4.10) couples the fields along gauge-fixing chains. Each chain originates from its own minimal-ghost vertex at the right slope and extends left-downward until the maximal level 𝑙 = 𝑝, with spi… view at source ↗
Figure 3
Figure 3. Figure 3: Splitting of a gauge-fixing chain A gauge-fixing chain, which originates from the minimal ghost 𝒞 0 𝜈[𝑟∘] and ends at 𝒞 𝑟∘ . The chain splits into two subchains of equations relating ghosts within 𝒞 𝑟∘−2𝑛 𝜈[2𝑛] and 𝒞 𝑟∘−1−2𝑛 𝜈[2𝑛+1] families. The configuration of the subchains’ endings depends on the parity of the chain’s length. (4.34), the first equation to solve is 𝛾𝜈𝑃 𝜈[2]𝜇[2] △ 𝒞𝜇[2]+𝛾 𝜈𝒞· = 0, which … view at source ↗
Figure 4
Figure 4. Figure 4: Table of determinants in effective action [PITH_FULL_IMAGE:figures/full_fig_p032_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Triangular diagram: BV fields and gauge fixing [PITH_FULL_IMAGE:figures/full_fig_p038_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Structure of the gauge-fixed action 37 [PITH_FULL_IMAGE:figures/full_fig_p038_6.png] view at source ↗

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Reference graph

Works this paper leans on

36 extracted references · 20 canonical work pages · cited by 2 Pith papers · 5 internal anchors

  1. [1]

    D-Branes

    C. V. Johnson, “D-Branes”, Cambridge University Press, 2003, 548 p

    work page 2003

  2. [2]

    Gravity and strings

    T. Ortin, “Gravity and strings”, Cambridge University Press, 2004, 684 p

    work page 2004

  3. [3]

    Supergravity

    D. Z. Freedman, A. Van Proeyen, “Supergravity”, Cambridge University Press, 2012, 607 p

    work page 2012

  4. [4]

    The notoph and its possible interactions

    V. I. Ogievetsky, I. V. Polubarinov, “The notoph and its possible interactions”, Yadernaya Fizika (Soviet Journal Nuclear Physics),4 (1967) 156

    work page 1967

  5. [5]

    Classical direct interstring action

    M. Kalb, P. Ramond, “Classical direct interstring action”, Phys. Rev. D9 (1974) 2273

    work page 1974

  6. [6]

    Gauge fields, nonlinear realizations, supersymmetry

    E. A. Ivanov, “Gauge fields, nonlinear realizations, supersymmetry”, Phys. Part. Nucl. 47 (2016) no.4, 508-539,arXiv:1604.01379 [hep-th]

    Pith/arXiv arXiv 2016

  7. [7]

    Antisymmetric tensor gauge fields and nonlinear sigma models

    D. Z. Freedman, P. K. Townsend, “Antisymmetric tensor gauge fields and nonlinear sigma models”, Nucl. Phys. B177 (1981) 282. 42For example, within the framework of restricted gauge theories, the use of full-rank gauge fixing allows one to establish a nontrivial relation between the one-loop effective actions of the restricted and parent gauge theories [36]. 39

    work page 1981

  8. [8]

    Quantum equivalence of massive antisym- metric tensor field models in curved space

    I. L. Buchbinder, E. N. Kirillova, N. G. Pletnev, “Quantum equivalence of massive antisym- metric tensor field models in curved space”, Phys. Rev. D78 (2008) 084024,arXiv:0806.3505 [hep-th]

    Pith/arXiv arXiv 2008

  9. [9]

    Covariant quantisation of tensor multiplet models

    S. M. Kuzenko, E. S. N. Raptakis, “Covariant quantisation of tensor multiplet models”, JHEP, 09 (2024) 182, arXiv:2406.01176 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  10. [10]

    The partition function of degenerate quadratic functionals and Ray-Singer invariants

    A. S. Schwarz, “The partition function of degenerate quadratic functionals and Ray-Singer invariants”, Lett. Math. Phys.2 (1978) 247

    work page 1978

  11. [11]

    The partition function of a degenerate functional

    A. S. Schwarz, “The partition function of a degenerate functional”, Commun. Math. Phys.67 (1979) 1

    work page 1979

  12. [12]

    Hidden ghosts

    W. Siegel, “Hidden ghosts”, Phys. Lett. B93 (1980), 170

    work page 1980

  13. [13]

    Quantization of the classically equivalent theories in the superspace of simple supergravity and quantum equivalence

    I. L. Buchbinder, S. M. Kuzenko, “Quantization of the classically equivalent theories in the superspace of simple supergravity and quantum equivalence”, Nucl. Phys. B308 (1988) 162

    work page 1988

  14. [14]

    Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS(d) space

    I. L. Buchbinder, V. A. Krykhtin, L. L. Ryskina, “Lagrangian formulation of massive fermionic totally antisymmetric tensor field theory in AdS(d) space”, Nucl. Phys. B819 (2009), 453-477, arXiv:0902.1471 [hep-th]

    Pith/arXiv arXiv 2009

  15. [15]

    Note on antisymmetric spin-tensors

    Yu. M. Zinoviev, “Note on antisymmetric spin-tensors”, JHEP 04 (2009), 035, arXiv:0903.0262 [hep-th]

    Pith/arXiv arXiv 2009

  16. [16]

    Unconstrained higher spins of mixed symmetry. II. Fermi fields

    A. Campoleoni, D. Francia, J. Mourad, A. Sagnotti, “Unconstrained higher spins of mixed symmetry. II. Fermi fields”, Nucl. Phys. B828 (2010) 405, arXiv:0904.4447 [hep-th]

    Pith/arXiv arXiv 2010

  17. [17]

    Stronly coupled gravity and dualities

    C. M. Hull, “Stronly coupled gravity and dualities”, Nucl. Phys. B 583 (2000) 237, arXiv:hep-th/0004195

    Pith/arXiv arXiv 2000

  18. [18]

    Symmetries and compactifications of (4,0) conformal gravity

    C. M. Hull, “Symmetries and compactifications of (4,0) conformal gravity”, JHEP12 (2000) 007, arXiv:hep-th/0011215

    Pith/arXiv arXiv 2000

  19. [19]

    E(11) and M theory

    P. West, “E(11) and M theory”, Class. Quant. Grav.18 (2001) 443, arXiv:hep-th/0104081

    Pith/arXiv arXiv 2001

  20. [20]

    Duality in gravity and higher spin gauge fields

    C. M. Hull, “Duality in gravity and higher spin gauge fields”, JHEP 09 (2001) 027, arXiv:hep-th/0107149

    Pith/arXiv arXiv 2001

  21. [21]

    𝐷 = 6 ,𝒩 = (2 , 0) and𝒩 = (4 , 0) theories

    L. Borsten, “𝐷 = 6 ,𝒩 = (2 , 0) and𝒩 = (4 , 0) theories”, Phys. Rev. D97 (2018) 066014, arXiv:1708.02573 [hep-th]

    Pith/arXiv arXiv 2018

  22. [22]

    The action of the (free) (4,0)-theory

    M. Henneaux, V. Lekeu, A. Leonard, “The action of the (free) (4,0)-theory”, JHEP01 (2018) 114, arXiv:1711.07448 [hep-th] , [erratum: JHEP05 (2018) 105]

    Pith/arXiv arXiv 2018

  23. [23]

    The action of the (free)𝒩 + (3, 1) theory in six spacetime dimensions

    M. Henneaux, V. Lekeu, J. Matulich, S. Prohazka, “The action of the (free)𝒩 + (3, 1) theory in six spacetime dimensions”, JHEP06 (2018) 057, arXiv:1804.10125 [hep-th]

    Pith/arXiv arXiv 2018

  24. [24]

    On symmetries and dynamics of exotic supermultiplets

    R. Minasian, C. Strickland-Constable, Y. Zhang, “On symmetries and dynamics of exotic supermultiplets”, arXiv:2007.08888 [hep-th]

    Pith/arXiv arXiv 2007

  25. [25]

    Towards exotic 6𝐷 supergravities

    Y. Bertrand, S. Hohenegger, O. Holm, H. Samtleben, “Towards exotic 6𝐷 supergravities”, Phys. Rev. D103 (2021) 046002, arXiv:2007.11644 [hep-th]

    Pith/arXiv arXiv 2021

  26. [26]

    Superspace formulation of exotic supergravities in six dimensions

    M. Cederwall, “Superspace formulation of exotic supergravities in six dimensions”, JHEP03 (2021) 056, arXiv:2012.02719 [hep-th] . 40

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  27. [27]

    Unified non-metric (1,0) tensor-Einstein supergravity theories and (4,0) supergravity in six dimensions

    M. Gunaydin, “Unified non-metric (1,0) tensor-Einstein supergravity theories and (4,0) super- gravity in six dimensions”, JHEP06 (2021) 081, arXiv:2009.01374 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  28. [28]

    Gauge algebra and quantization

    I. A. Batalin, G. A. Vilkovisky, “Gauge algebra and quantization”, Phys. Lett. B102 (1981) 27

    work page 1981

  29. [29]

    Quantization of gauge theories with linearly dependent gen- erators

    I. A. Batalin, G. A. Vilkovisky, “Quantization of gauge theories with linearly dependent gen- erators”, Phys. Rev. D28 (1983), 2567 [erratum: Phys. Rev. D30 (1984), 508]

    work page 1983

  30. [30]

    Hamiltonian form for the path integral for theories with a gauge freedom

    M. Henneaux, “Hamiltonian form for the path integral for theories with a gauge freedom”, Phys. Repts.126 (1985) 1

    work page 1985

  31. [31]

    Quantization of gauge systems

    M. Henneaux, C. Teitelboim, “Quantization of gauge systems”, Princeton Univ. Press, 1992, 552 p

    work page 1992

  32. [32]

    Antibracket, antifields and gauge theory quantization

    J. Gomis, J. Paris, S. Samuel, “Antibracket, antifields and gauge theory quantization”, Phys. Repts. 259 (1995) 1, arXiv:hep-th/9412228 [hep-th]

    Pith/arXiv arXiv 1995

  33. [33]

    Adjustment of Faddeev-Popov quantization to reducible gauge theories: antisymmetric tensor fermion in $AdS_d$ space

    A. O. Barvinsky, I. L. Buchbinder, V. A. Krykhtin, D. V. Nesterov, “Adjustment of Faddeev- Popov quantization to reducible gauge theories: antisymmetric tensor fermion in𝐴𝑑𝑆𝑑 space”, arXiv:2507.09312 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  34. [34]

    On the quantisation and anomalies of antisymmetric tensor-spinors

    V. Lekeu, Y. Zhang, “On the quantisation and anomalies of antisymmetric tensor-spinors”, JHEP 11 (2021), 078, arXiv:2109.03963 [hep-th]

    Pith/arXiv arXiv 2021

  35. [35]

    Harmonic analysis and propagators on homogeneous space

    R. Camporesi, “Harmonic analysis and propagators on homogeneous space”, Phys. Repts.196 (1990) 1

    work page 1990

  36. [36]

    Restricted Gauge Theory Formalism and Unimodular Gravity

    A. O. Barvinsky, D. V. Nesterov, “Restricted gauge theory formalism and unimodular gravity”, Phys. Rev. D108 (2023) no.6, 065004,arXiv:2212.13539 [hep-th] . 41

    work page internal anchor Pith review Pith/arXiv arXiv 2023

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.