arxiv: 2605.05336 · v1 · submitted 2026-05-06 · ✦ hep-th · gr-qc· hep-ph

Recognition: unknown

Wormholes and the imaginary distance bound

Juan Maldacena , Alexander Maloney , Brian McPeak

Authors on Pith no claims yet

Pith reviewed 2026-05-08 16:42 UTC · model grok-4.3

classification ✦ hep-th gr-qchep-ph

keywords wormholesimaginary couplingsdistance boundanalytic continuationstring theoryweak gravity conjectureAdS gravitycomplex metrics

0 comments

The pith

Wormholes set an upper bound on how far coupling constants can be taken to imaginary values.

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

The paper argues that simple wormhole solutions in gravity, featuring massless scalars at imaginary values, impose an imaginary distance bound. This bound caps the analytic continuation of the theory when those scalars are reinterpreted as coupling constants in flat or AdS settings. In concrete string theory examples, other effects such as string corrections or instabilities make the low-energy description invalid at or before this limit. The authors claim that mechanisms enforcing the bound are a general feature of string theories that contain wormholes, and that the bound sometimes matches the weak gravity conjecture or the Kontsevich-Segal-Witten condition on complex metrics.

Core claim

Some of the simplest wormhole solutions involve massless scalar fields that take imaginary values. Massless fields can be interpreted as coupling constants in asymptotically flat or asymptotically AdS gravity theories. Wormhole effects imply an imaginary distance bound, an upper limit for the analytic continuation of the theory to imaginary values of these couplings. In string theory examples, explicit effects render the low-energy theory invalid either before or precisely at this wormhole limit. The existence of such effects enforcing the distance bound is a general feature of string theories containing wormholes. In some cases the bounds coincide with the weak gravity conjecture and with a

What carries the argument

Wormhole solutions with imaginary massless scalar fields, reinterpreted as coupling constants, whose semiclassical effects enforce a cutoff on further imaginary analytic continuation.

If this is right

The low-energy effective theory becomes invalid past the imaginary distance bound.
Stringy effects or instabilities appear at or before the bound and prevent further continuation.
The bound aligns with the weak gravity conjecture in specific cases.
Wormhole-induced bounds are a universal feature in any string theory that includes wormholes.

Where Pith is reading between the lines

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

The bound may serve as a new consistency requirement for effective field theories coupled to gravity.
It suggests wormholes help define the edge of the string landscape by cutting off certain complex deformations.
Holographic models could be used to test whether the cutoff survives beyond semiclassical approximations.

Load-bearing premise

The semiclassical wormhole solutions with imaginary scalars remain relevant in the full quantum theory and genuinely enforce a hard cutoff on analytic continuation rather than being artifacts.

What would settle it

A consistent string theory or quantum gravity model in which the low-energy effective description remains valid and stable for imaginary couplings beyond the wormhole-derived bound.

read the original abstract

Some of the simplest wormhole solutions involve massless scalar fields that take imaginary values. Massless fields can be interpreted as coupling constants in asymptotically flat or asymptotically AdS gravity theories. We argue that wormhole effects imply an imaginary distance bound, an upper limit for the analytic continuation of the theory to imaginary values of these couplings. In string theory examples, we find explicit effects that render the low-energy theory invalid either before or precisely at this wormhole limit. We argue that the existence of such effects enforcing the distance bound is a general feature of string theories containing wormholes. In some cases, the bounds we discuss coincide with the weak gravity conjecture, and with the Kontsevich-Segal-Witten condition on complex metrics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Wormholes with imaginary scalars point to a plausible cutoff on analytic continuation, backed by string examples but still short on non-perturbative control.

read the letter

The core new idea is that simple wormhole solutions with massless scalars at imaginary values set an upper limit on how far couplings can be continued into the complex plane before the low-energy theory breaks down. In the string examples they work through, the actual physics invalidates the EFT at or before this wormhole limit, and the bound sometimes matches the weak gravity conjecture or the Kontsevich-Segal-Witten condition on complex metrics. That overlap is useful and gives the claim some teeth beyond pure speculation.

Referee Report

2 major / 2 minor

Summary. The paper argues that wormhole solutions in gravity theories involving massless scalar fields (interpreted as couplings) that take imaginary values imply an 'imaginary distance bound,' which limits analytic continuation of the theory into the complex coupling plane. In explicit string theory examples, the low-energy EFT is shown to break down at or before this bound. The authors claim this enforcement mechanism is a general feature of string theories containing wormholes and note coincidences with the weak gravity conjecture and the Kontsevich-Segal-Witten condition on complex metrics.

Significance. If the central claim holds, the work provides a novel link between semiclassical wormhole effects and bounds on complexified couplings, offering a potential non-perturbative mechanism within the swampland program. The concrete string theory examples add value by making the bound explicit, and the noted overlaps with WGC and KSW conditions suggest broader consistency. Strengths include the focus on massless scalars as couplings and the attempt to connect wormholes to analytic continuation limits.

major comments (2)

[Abstract] The core argument that semiclassical wormhole saddles with imaginary scalars enforce a hard cutoff on analytic continuation (as stated in the abstract) rests on an interpretation that these effects remain relevant and impose a genuine bound in the full quantum theory, rather than being artifacts of the semiclassical approximation; without a controlled non-perturbative computation or explicit demonstration of the cutoff mechanism, this assumption is load-bearing and requires further justification.
The generality claim that 'the existence of such effects enforcing the distance bound is a general feature of string theories containing wormholes' is supported only by specific examples; a more systematic argument or classification of wormhole solutions would be needed to establish that the bound is not an artifact of post-hoc example selection.

minor comments (2)

The precise mathematical definition of the 'imaginary distance bound' (e.g., in terms of a metric on coupling space) should be stated explicitly and early, rather than left implicit from the wormhole solutions.
Clarify the regime of validity of the semiclassical wormhole solutions when scalars are continued to imaginary values, including any assumptions about the effective theory cutoff.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We respond point by point to the major comments below, indicating planned revisions to the manuscript.

read point-by-point responses

Referee: [Abstract] The core argument that semiclassical wormhole saddles with imaginary scalars enforce a hard cutoff on analytic continuation (as stated in the abstract) rests on an interpretation that these effects remain relevant and impose a genuine bound in the full quantum theory, rather than being artifacts of the semiclassical approximation; without a controlled non-perturbative computation or explicit demonstration of the cutoff mechanism, this assumption is load-bearing and requires further justification.

Authors: We agree that the argument is grounded in the semiclassical approximation and that a controlled non-perturbative demonstration of the cutoff is not provided. The manuscript instead relies on explicit string theory examples in which the low-energy EFT is shown to break down at or before the wormhole bound through the appearance of light states or other inconsistencies. We will revise the abstract and relevant sections to clarify that the bound is suggested by semiclassical wormhole effects and is realized via explicit EFT breakdowns in the examples, rather than asserting a non-perturbative hard cutoff. revision: partial
Referee: The generality claim that 'the existence of such effects enforcing the distance bound is a general feature of string theories containing wormholes' is supported only by specific examples; a more systematic argument or classification of wormhole solutions would be needed to establish that the bound is not an artifact of post-hoc example selection.

Authors: We acknowledge that the generality statement is based on the specific examples analyzed rather than a complete classification of wormhole solutions. A systematic classification lies beyond the scope of the present work. In the revised manuscript we will weaken the claim to state that the bound is enforced in the examples considered and discuss the structural reasons tied to massless scalars in string compactifications, while noting that broader generality remains conjectural and merits further study. revision: yes

Circularity Check

0 steps flagged

No significant circularity: bound follows from semiclassical wormhole saddles and string examples

full rationale

The derivation starts from known semiclassical wormhole solutions involving massless scalars at imaginary values, interprets these as implying a cutoff on analytic continuation of couplings (the imaginary distance bound), and then checks explicit string theory realizations where the low-energy EFT is invalidated at or before the bound by other effects. This chain does not reduce any prediction to a fitted input or self-definition; the wormhole saddles are standard solutions in the Einstein-scalar theory and their cutoff interpretation is an additional physical claim, not a tautology. String examples supply independent enforcement mechanisms outside the wormhole analysis itself. No load-bearing self-citation chain or ansatz smuggling is required for the central argument. The paper is self-contained against external benchmarks such as the WGC and KSW conditions, which are only noted as coincidences rather than used as premises.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The argument relies on the existence and relevance of semiclassical wormhole solutions with imaginary scalars, plus standard assumptions of string theory embeddings. No explicit free parameters are named in the abstract. No new entities are postulated beyond the wormholes themselves.

axioms (2)

domain assumption Semiclassical wormhole solutions with imaginary massless scalars are physically meaningful saddles in the gravitational path integral.
Invoked to derive the bound from wormhole effects.
domain assumption The low-energy effective theory remains valid up to the point where stringy or other effects invalidate it.
Used to argue that the bound is enforced before or at the wormhole limit.

pith-pipeline@v0.9.0 · 5414 in / 1458 out tokens · 60153 ms · 2026-05-08T16:42:16.405857+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Breaking Free from the Swampland of Impossible Universes through the DESI Portal
astro-ph.CO 2026-05 unverdicted novelty 2.0

DESI data indicating evolving dark energy may allow string theory to describe observed universes without violating swampland constraints on constant dark energy.

Reference graph

Works this paper leans on

50 extracted references · 44 canonical work pages · cited by 1 Pith paper

[1]

A semiclassical ramp in SYK and in gravity

P. Saad, S.H. Shenker and D. Stanford,A semiclassical ramp in SYK and in gravity, 1806.06840

work page Pith review arXiv
[2]

Penington, S

G. Penington, S.H. Shenker, D. Stanford and Z. Yang,Replica wormholes and the black hole interior,JHEP03(2022) 205 [1911.11977]

work page arXiv 2022
[3]

Almheiri, T

A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini,Replica Wormholes and the Entropy of Hawking Radiation,JHEP05(2020) 013 [1911.12333]. – 44 –

work page arXiv 2020
[4]

Coleman,Black holes as red herrings: Topological fluctuations and the loss of quantum coherence,Nucl

S.R. Coleman,Black holes as red herrings: Topological fluctuations and the loss of quantum coherence,Nucl. Phys. B307(1988) 867

1988
[5]

Giddings and A

S.B. Giddings and A. Strominger,Axion Induced Topology Change in Quantum Gravity and String Theory,Nucl. Phys. B306(1988) 890

1988
[6]

JT gravity as a matrix integral

P. Saad, S.H. Shenker and D. Stanford,JT gravity as a matrix integral,1903.11115

work page Pith review arXiv 1903
[7]

Saad, S.H

P. Saad, S.H. Shenker, D. Stanford and S. Yao,Wormholes without averaging,JHEP 09(2024) 133 [2103.16754]

work page arXiv 2024
[8]

Arkani-Hamed, J

N. Arkani-Hamed, J. Orgera and J. Polchinski,Euclidean wormholes in string theory, JHEP12(2007) 018 [0705.2768]

work page arXiv 2007
[9]

Kontsevich and G

M. Kontsevich and G. Segal,Wick Rotation and the Positivity of Energy in Quantum Field Theory,Quart. J. Math. Oxford Ser.72(2021) 673 [2105.10161]

work page arXiv 2021
[10]

Witten,A Note On Complex Spacetime Metrics,2111.06514

E. Witten,A Note On Complex Spacetime Metrics,2111.06514

work page arXiv
[11]

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(2007) 060 [hep-th/0601001]

work page Pith review arXiv 2007
[12]

Witten,Duality and Axion Wormholes,2601.01587

E. Witten,Duality and Axion Wormholes,2601.01587

work page arXiv
[13]

J. Held, M. Kaplan, D. Marolf and Z. Wang,Axion Wormholes and the AdS/CFT Factorization Problem,2601.02507

work page arXiv
[14]

J. Held, M. Kaplan, D. Marolf and Z. Wang,Lorentzian Path Integrals and Jackiw-Teitelboim wormholes with imaginary scalars,2601.09932

work page arXiv
[15]

Hertog, B

T. Hertog, B. Truijen and T. Van Riet,Euclidean axion wormholes have multiple negative modes,Phys. Rev. Lett.123(2019) 081302 [1811.12690]

work page arXiv 2019
[16]

Loges, G

G.J. Loges, G. Shiu and N. Sudhir,Complex saddles and Euclidean wormholes in the Lorentzian path integral,JHEP08(2022) 064 [2203.01956]

work page arXiv 2022
[17]

Aguilar-Gutierrez, T

S.E. Aguilar-Gutierrez, T. Hertog, R. Tielemans, J.P. van der Schaar and T. Van Riet,Axion-de Sitter wormholes,JHEP11(2023) 225 [2306.13951]

work page arXiv 2023
[18]

Ivo and H

V. Ivo and H. Tang,One-loop aspects of de Sitter axion wormholes,2603.02335

work page arXiv
[19]

To appear

G. Di Ubaldo, L. Iliesiu, H.W. Lin and C. Yan, “To appear.”
[20]

Bergshoeff, A

E. Bergshoeff, A. Collinucci, U. Gran, D. Roest and S. Vandoren,Non-extremal D-instantons,JHEP10(2004) 031 [hep-th/0406038]

work page arXiv 2004
[21]

Bergshoeff, A

E. Bergshoeff, A. Collinucci, U. Gran, D. Roest and S. Vandoren,Non-extremal instantons and wormholes in string theory,Fortsch. Phys.53(2005) 990 [hep-th/0412183]

work page arXiv 2005
[22]

Bergshoeff, A

E. Bergshoeff, A. Collinucci, A. Ploegh, S. Vandoren and T. Van Riet,Non-extremal D-instantons and the AdS/CFT correspondence,JHEP01(2006) 061 [hep-th/0510048]

work page arXiv 2006
[23]

Vafa and E

C. Vafa and E. Witten,A Strong coupling test of S duality,Nucl. Phys. B431 (1994) 3 [hep-th/9408074]. – 45 –

work page arXiv 1994
[24]

Witten,Instability of the Kaluza-Klein Vacuum,Nucl

E. Witten,Instability of the Kaluza-Klein Vacuum,Nucl. Phys. B195(1982) 481

1982
[25]

García-García and V

A.M. García-García and V. Godet,Euclidean wormhole in the Sachdev-Ye-Kitaev model,Phys. Rev. D103(2021) 046014 [2010.11633]

work page arXiv 2021
[26]

Chakravarty, A

J. Chakravarty, A. Maloney, K. Namjou and S.F. Ross,A new observable for holographic cosmology,JHEP10(2024) 184 [2407.04781]

work page arXiv 2024
[27]

On the Geometry of the String Landscape and the Swampland

H. Ooguri and C. Vafa,On the Geometry of the String Landscape and the Swampland,Nucl. Phys. B766(2007) 21 [hep-th/0605264]

work page Pith review arXiv 2007
[28]

Grimm, E

T.W. Grimm, E. Palti and I. Valenzuela,Infinite Distances in Field Space and Massless Towers of States,JHEP08(2018) 143 [1802.08264]

work page arXiv 2018
[29]

Harlow, B

D. Harlow, B. Heidenreich, M. Reece and T. Rudelius,Weak gravity conjecture,Rev. Mod. Phys.95(2023) 035003 [2201.08380]

work page arXiv 2023
[30]

Heidenreich, M

B. Heidenreich, M. Reece and T. Rudelius,Sharpening the Weak Gravity Conjecture with Dimensional Reduction,JHEP02(2016) 140 [1509.06374]

work page arXiv 2016
[31]

Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,

T.G. Mertens and G.J. Turiaci,Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,Living Rev. Rel.26(2023) 4 [2210.10846]

work page arXiv 2023
[32]

Eternal traversable wormhole

J. Maldacena and X.-L. Qi,Eternal traversable wormhole,1804.00491

work page Pith review arXiv
[33]

Cheung and G.N

C. Cheung and G.N. Remmen,Naturalness and the Weak Gravity Conjecture,Phys. Rev. Lett.113(2014) 051601 [1402.2287]

work page arXiv 2014
[34]

Benetti Genolini, O

P. Benetti Genolini, O. Janssen and S. Murthy,Allowable complex metrics and the gravitational index of AdS5 black holes,2601.23197

work page arXiv
[35]

Lectures on Supergravity p-branes

K.S. Stelle,Lectures on supergravity p-branes, inICTP Summer School in High-energy Physics and Cosmology, pp. 287–339, 6, 1996 [hep-th/9701088]

work page Pith review arXiv 1996
[36]

Effects of D-instantons

M.B. Green and M. Gutperle,Effects of D instantons,Nucl. Phys. B498(1997) 195 [hep-th/9701093]

work page Pith review arXiv 1997
[37]

Gross and E

D.J. Gross and E. Witten,Superstring Modifications of Einstein’s Equations,Nucl. Phys. B277(1986) 1

1986
[38]

Green and J.H

M.B. Green and J.H. Schwarz,Supersymmetrical Dual String Theory. 3. Loops and Renormalization,Nucl. Phys. B198(1982) 441

1982
[39]

Eisenstein Series and String Thresholds

N.A. Obers and B. Pioline,Eisenstein series and string thresholds,Commun. Math. Phys.209(2000) 275 [hep-th/9903113]

work page Pith review arXiv 2000
[40]

Dimopoulos, S

S. Dimopoulos, S. Kachru, J. McGreevy and J.G. Wacker,N-flation,JCAP08 (2008) 003 [hep-th/0507205]

work page arXiv 2008
[41]

Vadacchino, C

D. Vadacchino, C. Bonanno, C. Bonati and M. Papace,The imaginary-θdependence of the SU(N) spectrum,PoSLA TTICE2024(2025) 399 [2411.14022]

work page arXiv 2025
[42]

Marolf and J

D. Marolf and J.E. Santos,AdS Euclidean wormholes,Class. Quant. Grav.38(2021) 224002 [2101.08875]

work page arXiv 2021
[43]

Maloney, V

A. Maloney, V. Meruliya and M. Van Raamsdonk,Ordinary wormholes,2503.12227. – 46 –

work page arXiv
[44]

Maldacena and L

J.M. Maldacena and L. Maoz,Wormholes in AdS,JHEP02(2004) 053 [hep-th/0401024]

work page arXiv 2004
[45]

Witten and S.-T

E. Witten and S.-T. Yau,Connectedness of the boundary in the AdS / CFT correspondence,Adv. Theor. Math. Phys.3(1999) 1635 [hep-th/9910245]

work page arXiv 1999
[46]

Lyth,What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?,Phys

D.H. Lyth,What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?,Phys. Rev. Lett.78(1997) 1861 [hep-ph/9606387]

work page arXiv 1997
[47]

Chang et al.,Snowmass2021 Cosmic Frontier: Cosmic Microwave Background Measurements White Paper,2203.07638

C.L. Chang et al.,Snowmass2021 Cosmic Frontier: Cosmic Microwave Background Measurements White Paper,2203.07638

work page arXiv
[48]

Rudelius,Constraints on Axion Inflation from the Weak Gravity Conjecture, JCAP09(2015) 020 [1503.00795]

T. Rudelius,Constraints on Axion Inflation from the Weak Gravity Conjecture, JCAP09(2015) 020 [1503.00795]

work page arXiv 2015
[49]

Brown, W

J. Brown, W. Cottrell, G. Shiu and P. Soler,Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation,JHEP10(2015) 023 [1503.04783]

work page arXiv 2015
[50]

Montero, A.M

M. Montero, A.M. Uranga and I. Valenzuela,Transplanckian axions!?,JHEP08 (2015) 032 [1503.03886]. – 47 –

work page arXiv 2015