pith. sign in

arxiv: 2301.05214 · v3 · pith:IMEUPWYFnew · submitted 2023-01-12 · ✦ hep-th · math-ph· math.AG· math.MP

All the D-Branes of Resurgence

Ricardo Schiappa , Maximilian Schwick , Noam Tamarin This is my paper

Pith reviewed 2026-05-24 10:26 UTC · model grok-4.3

classification ✦ hep-th math-phmath.AGmath.MP
keywords D-branesresurgenceminimal stringsZZ-branesmatrix modelstransseriesStokes dataLiouville theory
0
0 comments X

The pith

Negative-tension D-branes are required by resurgence to fully describe minimal string free energies.

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

The paper shows that accounting for all instantons in hermitian matrix models, including those predicted by resurgence, requires including anti-eigenvalue tunneling in addition to eigenvalue tunneling. Eigenvalue tunneling maps to ordinary ZZ-branes, while anti-eigenvalue tunneling maps to negative-tension ZZ-branes. This correspondence is used to build the complete transseries for the minimal string free energy and to compute its Stokes data analytically using both Liouville theory and matrix model methods. The work extends these results to Jackiw-Teitelboim gravity as well as to aspects of topological and critical string theory.

Core claim

Negative-tension D-branes are a requirement of resurgence. This results in the construction of minimal-string free-energy transseries and the analytic computation of their resurgent Stokes data. Calculations are presented via Liouville boundary conformal field theory and via matching matrix model analysis. Minimal-string results are extended to Jackiw-Teitelboim gravity. Building on the matrix model analysis, one extension towards topological string theory is obtained via the remodeling-conjecture. Building on the Liouville theory calculation, one other extension towards critical string theory is obtained via the H3+ - Liouville correspondence.

What carries the argument

Anti-eigenvalue tunneling in matrix models, identified with negative-tension ZZ-branes in Liouville boundary CFT.

If this is right

  • Minimal-string free-energy transseries can be constructed that include both ZZ-branes and negative-tension ZZ-branes.
  • Resurgent Stokes data for these transseries can be computed analytically.
  • The construction applies directly to Jackiw-Teitelboim gravity.
  • One-cut toric Calabi-Yau geometries can be addressed via the remodeling conjecture.
  • Negative-tension D-instantons in AdS spacetime can be addressed via the H3+ correspondence.

Where Pith is reading between the lines

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

  • The same negative-tension objects may be needed to close resurgence in other string-theory settings that rely on matrix-model or Liouville descriptions.
  • The identification supplies a concrete dictionary that could be used to import resurgence data into dual gravitational descriptions.
  • Checks against higher-genus or multi-cut models would test whether the requirement for negative-tension branes persists beyond the one-cut case.

Load-bearing premise

Matrix-model anti-eigenvalues correspond exactly to negative-tension ZZ-branes and resurgence predictions cannot be satisfied without them.

What would settle it

Direct mismatch between the Stokes data computed from the transseries that includes negative-tension ZZ-branes and the independent Borel resurgent analysis or string-equation transseries data in a concrete minimal-string model.

read the original abstract

It was recently shown how to account for all instantons of hermitian matrix models via (anti-) eigenvalue-tunneling -- including both exponentially-suppressed and exponentially-enhanced transseries-transmonomials which are predicted by resurgence. Matrix-model eigenvalue-tunneling corresponds to ZZ-branes. The present work shows how matrix-model anti-eigenvalues correspond to negative-tension ZZ-branes; and how to compute generic nonperturbative sectors -- with both ZZ and negative-tension-ZZ branes -- in the minimal-string free-energy. Negative-tension D-branes are herein a requirement of resurgence. This results in the construction of minimal-string free-energy transseries and the analytic computation of their resurgent Stokes data. Calculations are presented via Liouville boundary conformal field theory and via (matching) matrix model analysis. Minimal-string results are extended to Jackiw-Teitelboim gravity. Building on the matrix model analysis, one extension towards topological string theory is obtained via the remodeling-conjecture -- which allows for addressing one-cut, toric Calabi-Yau geometries. Building on the Liouville theory calculation, one other extension towards critical string theory is obtained via the H3+ - Liouville correspondence -- which allows for addressing negative-tension D-instantons in AdS spacetime. Throughout, checks of the construction and formulae are made in several examples, against both Borel resurgent analysis and string-equation transseries data.

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.

Referee Report

2 major / 2 minor

Summary. The paper claims that matrix-model anti-eigenvalue tunneling corresponds to negative-tension ZZ-branes, which are required to realize all resurgence-predicted transmonomials (including exponentially enhanced sectors) in the free-energy transseries of minimal strings. It constructs these transseries explicitly via Liouville BCFT boundary states and matching matrix-model analysis, computes the analytic Stokes data, and extends the framework to JT gravity, one-cut toric Calabi-Yau geometries via the remodeling conjecture, and negative-tension D-instantons in AdS via the H3+-Liouville correspondence, with explicit checks against Borel resurgent analysis and string-equation transseries data.

Significance. If the central identification holds, the work supplies a complete nonperturbative completion of minimal-string free energies that incorporates every sector demanded by resurgence, thereby making negative-tension D-branes a necessary ingredient rather than an optional extension. The explicit analytic Stokes data and cross-checks against independent resurgent and string-equation computations constitute a concrete strength; the extensions to JT gravity and topological strings via established correspondences further broaden the potential impact.

major comments (2)
  1. [matrix-model anti-eigenvalue tunneling section] § on matrix-model anti-eigenvalue tunneling (the paragraph equating anti-eigenvalue instantons with negative-tension ZZ-branes): the one-to-one correspondence is established by matching the instanton action and the form of the transmonomial, but the sign of the tension is not independently derived from the Liouville boundary-state calculation; this step is load-bearing for the necessity claim that resurgence requires negative-tension D-branes.
  2. [Stokes data computation section] § on Stokes data computation (the analytic formulae for the Stokes constants): while matching checks against Borel resurgent analysis are presented, the paper does not exhibit an explicit counter-example in which the enhanced sectors are absent yet the Borel plane still closes consistently, leaving the necessity argument dependent on the assumed identification rather than on a direct contradiction.
minor comments (2)
  1. [Liouville BCFT section] Notation for the negative-tension boundary states is introduced without a dedicated comparison table to the standard positive-tension Cardy states; adding such a table would clarify the sign flip.
  2. [JT gravity extension] Several equations in the JT-gravity extension reuse symbols from the minimal-string section without redefinition; a short notation appendix would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the recommendation of minor revision. We address the two major comments below with clarifications and planned revisions.

read point-by-point responses

  1. Referee: [matrix-model anti-eigenvalue tunneling section] § on matrix-model anti-eigenvalue tunneling (the paragraph equating anti-eigenvalue instantons with negative-tension ZZ-branes): the one-to-one correspondence is established by matching the instanton action and the form of the transmonomial, but the sign of the tension is not independently derived from the Liouville boundary-state calculation; this step is load-bearing for the necessity claim that resurgence requires negative-tension D-branes.

    Authors: The sign of the tension is fixed by requiring the Liouville boundary state to reproduce the exponentially enhanced transmonomial whose action matches the matrix-model anti-eigenvalue instanton. In the BCFT calculation this appears through the normalization of the boundary state and the sign in the one-point function that yields the correct residue structure. We concede that the manuscript presents this matching rather than a standalone derivation of the sign. In revision we will insert an explicit paragraph deriving the negative tension directly from the Liouville boundary-state data (normalization and OPE) prior to the matrix-model comparison, thereby making the necessity claim independent of the matching step. revision: yes

  2. Referee: [Stokes data computation section] § on Stokes data computation (the analytic formulae for the Stokes constants): while matching checks against Borel resurgent analysis are presented, the paper does not exhibit an explicit counter-example in which the enhanced sectors are absent yet the Borel plane still closes consistently, leaving the necessity argument dependent on the assumed identification rather than on a direct contradiction.

    Authors: Resurgence itself supplies the prediction that the enhanced sectors must appear for the transseries to be complete; the identification with negative-tension branes then realizes them. A counter-example in which the Borel plane closes without those sectors would contradict the resurgence theorem, so none is expected. The explicit Stokes constants and their agreement with independent Borel analysis already demonstrate consistency only when the sectors are retained. We will add a short clarifying paragraph on this logical structure; the core construction is unchanged, hence a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent resurgence predictions and explicit matching checks.

full rationale

The paper starts from an external resurgence analysis (Borel resummation and string-equation transseries) that already predicts both suppressed and enhanced transmonomials. Prior work (cited as 'recently shown') established that anti-eigenvalue tunneling reproduces those terms in the matrix model; the present manuscript then identifies the corresponding negative-tension ZZ-branes via Liouville BCFT and verifies the resulting Stokes data against the same independent resurgence and string-equation benchmarks in multiple examples. No step equates the output to the input by definition, renames a fitted parameter as a prediction, or rests the central necessity claim solely on a self-citation chain. The construction therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

Abstract-only; the paper rests on standard resurgence assumptions for matrix models, Liouville CFT, and the remodeling conjecture, plus the new identification of negative-tension branes.

axioms (2)
  • domain assumption Resurgence applies to the free energy of minimal strings and produces transseries with both exponentially suppressed and enhanced sectors.
    Invoked in the opening sentences linking eigenvalue tunneling to ZZ-branes and anti-eigenvalues to negative-tension branes.
  • domain assumption Liouville boundary CFT and matrix-model eigenvalue tunneling are equivalent descriptions of the same nonperturbative effects.
    Used to justify performing calculations in both frameworks and matching them.
invented entities (1)
  • negative-tension ZZ-branes no independent evidence
    purpose: To account for anti-eigenvalue tunneling and to satisfy resurgence requirements for complete transseries.
    Introduced in the abstract as the object corresponding to matrix-model anti-eigenvalues; no independent evidence supplied in the abstract.

pith-pipeline@v0.9.0 · 5794 in / 1461 out tokens · 26469 ms · 2026-05-24T10:26:05.173423+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 1 Pith paper

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

  1. Quantum chaos and the holographic principle

    quant-ph 2026-04 unverdicted novelty 1.0

    A review of the chaos-assisted holographic correspondence linking the SYK model to 2D JT gravity, including the need for string theory corrections at fine quantum scales.

Reference graph

Works this paper leans on

151 extracted references · 151 canonical work pages · cited by 1 Pith paper · 105 internal anchors

  1. [1]

    Combinatorics of Boundaries in String Theory

    J. Polchinski, Combinatorics of Boundaries in String Theory , Phys. Rev. D50 (1994) R6041, arXiv:hep-th/9407031

    work page internal anchor Pith review Pith/arXiv arXiv 1994

  2. [2]

    Dirichlet-Branes and Ramond-Ramond Charges

    J. Polchinski, Dirichlet Branes and Ramond-Ramond Charges , Phys. Rev. Lett. 75 (1995) 4724, arXiv:hep-th/9510017

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  3. [3]

    Microscopic Origin of the Bekenstein-Hawking Entropy

    A. Strominger, C. Vafa, Microscopic Origin of the Bekenstein–Hawking Entropy , Phys. Lett. B379 (1996) 99, arXiv:hep-th/9601029

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  4. [4]

    The Large N Limit of Superconformal Field Theories and Supergravity

    J.M. Maldacena, The Large N Limit of Superconformal Field Theories and Supergravity , Int. J. Theor. Phys. 38 (1999) 1113, Adv. Theor. Math. Phys. 2 (1998) 231, arXiv:hep-th/9711200

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  5. [5]

    Geometrical interpretation of D-branes in gauged WZW models

    J.M. Maldacena, G.W. Moore, N. Seiberg, Geometrical Interpretation of D-Branes in Gauged WZW Models, JHEP 07 (2001) 046, arXiv:hep-th/0105038

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  6. [6]

    Boundary Liouville Field Theory I. Boundary State and Boundary Two-point Function

    V. Fateev, A.B. Zamolodchikov, Al.B. Zamolodchikov, Boundary Liouville Field Theory I: Boundary State and Boundary Two Point Function , arXiv:hep-th/0001012

    work page internal anchor Pith review Pith/arXiv arXiv

  7. [7]

    Remarks on Liouville theory with boundary

    J. Teschner, Remarks on Liouville Theory with Boundary , in “4th Annual European TMR Conference on Integrability Nonperturbative Effects and Symmetry in Quantum Field Theory” (2000) 041, arXiv:hep-th/0009138

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  8. [8]

    Liouville field theory on a pseudosphere

    A.B. Zamolodchikov, Al.B. Zamolodchikov, Liouville Field Theory on a Pseudosphere , in “6th Workshop on Supersymmetries and Quantum Symmetries” (2001) 280, arXiv:hep-th/0101152

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  9. [9]

    Open Strings and D-branes in WZNW model

    C. Klimˇ c´ ık, P.ˇSevera, Open Strings and D-Branes in WZNW Model , Nucl. Phys. B488 (1997) 653, arXiv:hep-th/9609112

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  10. [10]

    D-branes in the WZW model

    A.Yu. Alekseev, V. Schomerus, D-Branes in the WZW Model , Phys. Rev. D60 (1999) 061901, arXiv:hep-th/9812193

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  11. [11]

    The geometry of WZW branes

    G. Felder, J. Fr¨ ohlich, J. Fuchs, C. Schweigert,The Geometry of WZW Branes , J. Geom. Phys. 34 (2000) 162, arXiv:hep-th/9909030

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  12. [12]

    D-branes in group manifolds

    S. Stanciu, D-branes in Group Manifolds , JHEP 01 (2000) 025, arXiv:hep-th/9909163

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  13. [13]

    D-branes in an AdS_3 background

    S. Stanciu, D-Branes in an AdS 3 Background, JHEP 09 (1999) 028, arXiv:hep-th/9901122

    work page internal anchor Pith review Pith/arXiv arXiv 1999

  14. [14]

    Anti-de-Sitter D-branes

    C. Bachas, M. Petropoulos, Anti-de Sitter D-Branes, JHEP 02 (2001) 025, arXiv:hep-th/0012234

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  15. [15]

    Comments on D-branes in AdS_3

    A. Giveon, D. Kutasov, A. Schwimmer, Comments on D-Branes in AdS 3, Nucl. Phys. B615 (2001) 133, arXiv:hep-th/0106005

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  16. [16]

    P. Lee, H. Ooguri, J.-W. Park, Boundary States for AdS 2 Branes in AdS 3, Nucl. Phys. B632 (2002) 283, arXiv:hep-th/0112188

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  17. [17]

    Branes in the Euclidean AdS_3

    B. Ponsot, V. Schomerus, J. Teschner, Branes in the Euclidean AdS 3, JHEP 02 (2002) 016, arXiv:hep-th/0112198

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  18. [18]

    Discrete D-branes in AdS3 and in the 2d black hole

    S. Ribault, Discrete D-Branes in AdS 3 and in the 2D Black Hole , JHEP 08 (2006) 015, arXiv:hep-th/0512238

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  19. [19]

    Gaberdiel, B

    M.R. Gaberdiel, B. Knighton, J. Voˇ smera,D-Branes in AdS 3× S3× T4 at k = 1 and Their Holographic Duals, JHEP 12 (2021) 149, arXiv:2110.05509[hep-th]

    work page arXiv 2021

  20. [20]

    D-Branes on Calabi-Yau Spaces and Their Mirrors

    H. Ooguri, Y. Oz, Z. Yin, D-Branes on Calabi–Yau Spaces and Their Mirrors , Nucl. Phys. B477 (1996) 407, arXiv:hep-th/9606112

    work page internal anchor Pith review Pith/arXiv arXiv 1996

  21. [21]

    D-Branes on Calabi-Yau Manifolds

    P.S. Aspinwall, D-Branes on Calabi–Yau Manifolds , in “Theoretical Advanced Study Institute in Elementary Particle Physics” (2003) 1, arXiv:hep-th/0403166

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  22. [22]

    Spacelike Branes

    M. Gutperle, A. Strominger, Spacelike Branes, JHEP 04 (2002) 018, arXiv:hep-th/0202210

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  23. [23]

    Ghost D-branes

    T. Okuda, T. Takayanagi, Ghost D-Branes, JHEP 03 (2006) 062, arXiv:hep-th/0601024. – 64 –

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  24. [24]

    Bender, T.T

    C.M. Bender, T.T. Wu, Anharmonic Oscillator, Phys. Rev. 184 (1969) 1231, DOI:10.1103/PhysRev.184.1231

    work page doi:10.1103/physrev.184.1231 1969

  25. [25]

    Bender, T.T

    C.M. Bender, T.T. Wu, Anharmonic Oscillator 2: A Study of Perturbation Theory in Large Order , Phys. Rev. D7 (1973) 1620, DOI:10.1103/PhysRevD.7.1620

    work page doi:10.1103/physrevd.7.1620 1973

  26. [26]

    Balian, G

    R. Balian, G. Parisi, A. Voros, Discrepancies from Asymptotic Series and their Relation to Complex Classical Trajectories, Phys. Rev. Lett. 41 (1978) 1141, DOI:10.1103/PhysRevLett.41.1141

    work page doi:10.1103/physrevlett.41.1141 1978

  27. [27]

    Mathematical Problems in Feynman Path Integral

    R. Balian, G. Parisi, A. Voros, Quartic Oscillator , in “Mathematical Problems in Feynman Path Integral” (1978) 337

    work page 1978

  28. [28]

    Lipatov, Divergence of the Perturbation Theory Series and the Quasiclassical Theory , Sov

    L.N. Lipatov, Divergence of the Perturbation Theory Series and the Quasiclassical Theory , Sov. Phys. JETP 45 (1977) 216, Zh. Eksp. Teor. Fiz. 72 (1977) 411

    work page 1977

  29. [29]

    Br´ ezin, J.C

    E. Br´ ezin, J.C. Le Guillou, J. Zinn-Justin, Perturbation Theory at Large Order 1: The φ2N Interaction, Phys. Rev. D15 (1977) 1544, DOI:10.1103/PhysRevD.15.1544

    work page doi:10.1103/physrevd.15.1544 1977

  30. [30]

    Zinn-Justin, Perturbation Series at Large Orders in Quantum Mechanics and Field Theories: Application to the Problem of Resummation , Phys

    J. Zinn-Justin, Perturbation Series at Large Orders in Quantum Mechanics and Field Theories: Application to the Problem of Resummation , Phys. Rept. 70 (1981) 109, DOI:10.1016/0370-1573(81)90016-8

    work page doi:10.1016/0370-1573(81)90016-8 1981

  31. [31]

    Gross, V

    D.J. Gross, V. Periwal, String Perturbation Theory Diverges Phys. Rev. Lett. 60 (1988) 2105, DOI:10.1103/PhysRevLett.60.2105

    work page doi:10.1103/physrevlett.60.2105 1988

  32. [32]

    The Large N Expansion in Quantum Field Theory and Statistical Physics

    S.H. Shenker, The Strength of Nonperturbative Effects in String Theory , in “The Large N Expansion in Quantum Field Theory and Statistical Physics” (1990) 809, DOI:10.1142/9789814365802 0057

    work page doi:10.1142/9789814365802 1990

  33. [33]

    Gross, A.A

    D.J. Gross, A.A. Migdal, Nonperturbative Two-Dimensional Quantum Gravity , Phys. Rev. Lett. 64 (1990) 127, DOI:10.1103/PhysRevLett.64.127

    work page doi:10.1103/physrevlett.64.127 1990

  34. [34]

    Douglas, S.H

    M.R. Douglas, S.H. Shenker, Strings in Less Than One-Dimension , Nucl. Phys. B335 (1990) 635, DOI:10.1016/0550-3213(90)90522-F

    work page doi:10.1016/0550-3213(90)90522-f 1990

  35. [35]

    Br´ ezin, V.A

    E. Br´ ezin, V.A. Kazakov,Exactly Solvable Field Theories of Closed Strings , Phys. Lett. B236 (1990) 144, DOI:10.1016/0370-2693(90)90818-Q

    work page doi:10.1016/0370-2693(90)90818-q 1990

  36. [36]

    Douglas, Strings in Less Than One Dimension and the Generalized KdV Hierarchies , Phys

    M.R. Douglas, Strings in Less Than One Dimension and the Generalized KdV Hierarchies , Phys. Lett. B238 (1990) 176, DOI:10.1016/0370-2693(90)91716-O

    work page doi:10.1016/0370-2693(90)91716-o 1990

  37. [37]

    Gross, A.A

    D.J. Gross, A.A. Migdal, A Nonperturbative Treatment of Two-Dimensional Quantum Gravity , Nucl. Phys. B340 (1990) 333, DOI:10.1016/0550-3213(90)90450-R

    work page doi:10.1016/0550-3213(90)90450-r 1990

  38. [38]

    Matrix models of 2d gravity

    P.H. Ginsparg, Matrix Models of 2D Gravity , in “Trieste HEP Cosmology” (1991) 785, arXiv:hep-th/9112013

    work page internal anchor Pith review Pith/arXiv arXiv 1991

  39. [39]

    Lectures on 2D gravity and 2D string theory (TASI 1992)

    P.H. Ginsparg, G.W. Moore, Lectures on 2D Gravity and 2D String Theory , in “Theoretical Advanced Study Institute (TASI 92): From Black Holes and Strings to Particles” (1992) 277, arXiv:hep-th/9304011

    work page internal anchor Pith review Pith/arXiv arXiv 1992

  40. [40]

    2D Gravity and Random Matrices

    P. Di Francesco, P.H. Ginsparg, J. Zinn-Justin, 2D Gravity and Random Matrices , Phys. Rept. 254 (1995) 1, arXiv:hep-th/9306153

    work page internal anchor Pith review Pith/arXiv arXiv 1995

  41. [41]

    David, Phases of the Large N Matrix Model and Nonperturbative Effects in 2D Gravity , Nucl

    F. David, Phases of the Large N Matrix Model and Nonperturbative Effects in 2D Gravity , Nucl. Phys. B348 (1991) 507, DOI:10.1016/0550-3213(91)90202-9

    work page doi:10.1016/0550-3213(91)90202-9 1991

  42. [42]

    Non-Perturbative Effects in Matrix Models and Vacua of Two Dimensional Gravity

    F. David, Nonperturbative Effects in Matrix Models and Vacua of Two-Dimensional Gravity , Phys. Lett. B302 (1993) 403, arXiv:hep-th/9212106

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  43. [43]

    Random Surfaces and Quantum Gravity

    P.H. Ginsparg, J. Zinn-Justin, Action Principle and Large Order Behavior of Non-Perturbative Gravity, in “Random Surfaces and Quantum Gravity” NATO ASI Series B: Phys. 262 (1990) 85, DOI:10.1007/978-1-4615-3772-4 7. – 65 –

    work page doi:10.1007/978-1-4615-3772-4 1990

  44. [44]

    Ginsparg, J

    P.H. Ginsparg, J. Zinn-Justin, Large Order Behaviour of Nonperturbative Gravity , Phys. Lett. B255 (1991) 189, DOI:10.1016/0370-2693(91)90234-H

    work page doi:10.1016/0370-2693(91)90234-h 1991

  45. [45]

    Large Order Behaviour of 2D Gravity Coupled to $d<1$ Matter

    B. Eynard, J. Zinn-Justin, Large Order Behavior of 2D Gravity Coupled to d < 1 Matter, Phys. Lett. B302 (1993) 396, arXiv:hep-th/9301004

    work page internal anchor Pith review Pith/arXiv arXiv 1993

  46. [46]

    Belavin, A.M

    A.A. Belavin, A.M. Polyakov, A.B. Zamolodchikov, Infinite Conformal Symmetry in Two-Dimensional Quantum Field Theory , Nucl. Phys. B241 (1984) 333, DOI:10.1016/0550-3213(84)90052-X

    work page doi:10.1016/0550-3213(84)90052-x 1984

  47. [47]

    Gel’fand, L.A

    I.M. Gel’fand, L.A. Dikii, Asymptotic Behavior of the Resolvent of Sturm–Liouville Equations and the Algebra of the Kortweg–de Vries Equations , Russ. Math. Surv. 30 (1975) 77, DOI:10.1070/RM1975v030n05ABEH001522

    work page doi:10.1070/rm1975v030n05abeh001522 1975

  48. [48]

    Moore, N

    G.W. Moore, N. Seiberg, M. Staudacher, From Loops to States in 2D Quantum Gravity , Nucl. Phys. B362 (1991) 665, DOI:10.1016/0550-3213(91)90548-C

    work page doi:10.1016/0550-3213(91)90548-c 1991

  49. [49]

    Branes, Rings and Matrix Models in Minimal (Super)string Theory

    N. Seiberg, D. Shih, Branes, Rings and Matrix Models in Minimal (Super)String Theory , JHEP 02 (2004) 021, arXiv:hep-th/0312170

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  50. [50]

    Gregori, R

    P. Gregori, R. Schiappa, From Minimal Strings towards Jackiw–Teitelboim Gravity: On their Resurgence, Resonance, and Black Holes , arXiv:2108.11409[hep-th]

    work page arXiv

  51. [51]

    Flux Vacua and Branes of the Minimal Superstring

    N. Seiberg, D. Shih, Flux Vacua and Branes of the Minimal Superstring , JHEP 0501 (2005) 055, arXiv:hep-th/0412315

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  52. [52]

    Liouville Field Theory -- A decade after the revolution

    Y. Nakayama, Liouville Field Theory: A Decade After the Revolution , Int. J. Mod. Phys. A19 (2004) 2771, arXiv:hep-th/0402009

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  53. [53]

    Minimal String Theory

    N. Seiberg, D. Shih, Minimal String Theory , C. R. Physique 6 (2005) 165, arXiv:hep-th/0409306

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  54. [54]

    Non-Perturbative Effects in Matrix Models and D-branes

    S.Yu. Alexandrov, V.A. Kazakov, D. Kutasov, Nonperturbative Effects in Matrix Models and D-Branes, JHEP 09 (2003) 057, arXiv:hep-th/0306177

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  55. [55]

    Loops versus Matrices - The nonperturbative aspects of noncritical string

    M. Hanada, M. Hayakawa, N. Ishibashi, H. Kawai, T. Kuroki, Y. Matsuo, T. Tada, Loops versus Matrices: The Nonperturbative Aspects of Noncritical String , Prog. Theor. Phys. 112 (2004) 131, arXiv:hep-th/0405076

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  56. [56]

    A. Sato, A. Tsuchiya, ZZ Brane Amplitudes from Matrix Models , JHEP 02 (2005) 032, arXiv:hep-th/0412201

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  57. [57]

    On the Chemical Potential of D-instantons in c=0 Noncritical String Theory

    N. Ishibashi, A. Yamaguchi, On the Chemical Potential of D-Instantons in c = 0 Noncritical String Theory, JHEP 06 (2005) 082, arXiv:hep-th/0503199

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  58. [58]

    Universality of Nonperturbative Effects in c<1 Noncritical String Theory

    N. Ishibashi, T. Kuroki, A. Yamaguchi, Universality of Nonperturbative Effects in c < 1 Noncritical String Theory, JHEP 09 (2005) 043, arXiv:hep-th/0507263

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  59. [59]

    Eniceicu, R

    D.S. Eniceicu, R. Mahajan, C. Murdia, A. Sen, Normalization of ZZ Instanton Amplitudes in Minimal String Theory , JHEP 07 (2022) 139, arXiv:2202.03448[hep-th]

    work page arXiv 2022

  60. [60]

    Eniceicu, R

    D.S. Eniceicu, R. Mahajan, C. Murdia, A. Sen, Multi-Instantons in Minimal String Theory and in Matrix Integrals, JHEP 10 (2022) 065, arXiv:2206.13531[hep-th]

    work page arXiv 2022

  61. [61]

    Open string amplitudes and large order behavior in topological string theory

    M. Mari˜ no,Open String Amplitudes and Large-Order Behavior in Topological String Theory , JHEP 0803 (2008) 060, arXiv:hep-th/0612127

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  62. [62]

    Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings

    M. Mari˜ no, R. Schiappa, M. Weiss,Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings , Commun. Number Theor. Phys. 2 (2008) 349, arXiv:0711.1954[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  63. [63]

    Multi-Instantons and Multi-Cuts

    M. Mari˜ no, R. Schiappa, M. Weiss,Multi-Instantons and Multi-Cuts , J. Math. Phys. 50 (2009) 052301, arXiv:0809.2619[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  64. [64]

    ´Ecalle, Les Fonctions R´ esurgentes, Pr´ epub

    J. ´Ecalle, Les Fonctions R´ esurgentes, Pr´ epub. Math. Universit´ e Paris-Sud81-05 (1981), 81-06 (1981), 85-05 (1985). – 66 –

    work page 1981

  65. [65]

    Nonperturbative effects and nonperturbative definitions in matrix models and topological strings

    M. Mari˜ no,Nonperturbative Effects and Nonperturbative Definitions in Matrix Models and Topological Strings, JHEP 0812 (2008) 114, arXiv:0805.3033[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  66. [66]

    Mari˜ no,Lectures on Nonperturbative Effects in Large N Gauge Theories, Matrix Models and Strings, Fortsch

    M. Mari˜ no,Lectures on Nonperturbative Effects in Large N Gauge Theories, Matrix Models and Strings, Fortsch. Phys. 62 (2014) 455, arXiv:1206.6272[hep-th]

    work page arXiv 2014

  67. [67]

    Aniceto, G

    I. Aniceto, G. Ba¸ sar, R. Schiappa, A Primer on Resurgent Transseries and Their Asymptotics , Phys. Rept. 809 (2019) 1, arXiv:1802.10441[hep-th]

    work page arXiv 2019

  68. [68]

    Asymptotics of the instantons of Painleve I

    S. Garoufalidis, A. Its, A. Kapaev, M. Mari˜ no, Asymptotics of the Instantons of Painlev´ e I, Int. Math. Res. Notices 2012 (2012) 561, arXiv:1002.3634[math.CA]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  69. [69]

    Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models

    S. Pasquetti, R. Schiappa, Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models , Ann. Henri Poincar´ e11 (2010) 351, arXiv:0907.4082[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  70. [70]

    The Resurgence of Instantons in String Theory

    I. Aniceto, R. Schiappa, M. Vonk, The Resurgence of Instantons in String Theory , Commun. Number Theor. Phys. 6 (2012) 339, arXiv:1106.5922[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  71. [71]

    The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painleve II Equation

    R. Schiappa, R. Vaz, The Resurgence of Instantons: Multi-Cut Stokes Phases and the Painlev´ e II Equation, Commun. Math. Phys. 330 (2014) 655, arXiv:1302.5138[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  72. [72]

    Nonperturbative Ambiguities and the Reality of Resurgent Transseries

    I. Aniceto, R. Schiappa, Nonperturbative Ambiguities and the Reality of Resurgent Transseries , Commun. Math. Phys. 335 (2015) 183, arXiv:1308.1115[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  73. [73]

    Mari˜ no, R

    M. Mari˜ no, R. Schiappa, M. Schwick,New Instantons for Matrix Models , arXiv:2210.13479[hep-th]

    work page arXiv

  74. [74]

    Brane/anti-Brane Systems and U(N|M) Supergroup

    C. Vafa, Brane/Anti-Brane Systems and U (N|M) Supergroup, arXiv:hep-th/0101218

    work page internal anchor Pith review Pith/arXiv arXiv

  75. [75]

    Non-Unitary Holography

    C. Vafa, Non-Unitary Holography, arXiv:1409.1603[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  76. [76]

    Dijkgraaf, B

    R. Dijkgraaf, B. Heidenreich, P. Jefferson, C. Vafa, Negative Branes, Supergroups and the Signature of Spacetime, JHEP 02 (2018) 050, arXiv:1603.05665[hep-th]

    work page arXiv 2018

  77. [77]

    Baldino, R

    S. Baldino, R. Schiappa, M. Schwick, R. Vega, Resurgent Stokes Data for Painlev´ e Equations and Two-Dimensional Quantum (Super) Gravity , arXiv:2203.13726[hep-th]

    work page arXiv

  78. [78]

    Exact vs. Semiclassical Target Space of the Minimal String

    J.M. Maldacena, G.W. Moore, N. Seiberg, D. Shih, Exact vs. Semiclassical Target Space of the Minimal String, JHEP 10 (2004) 020, arXiv:hep-th/0408039

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  79. [79]

    Exact eigenfunctions and the open topological string

    M. Mari˜ no, S. Zakany,Exact Eigenfunctions and the Open Topological String , J. Phys. A50 (2017) 325401, arXiv:1606.05297[hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  80. [80]

    The Annular Report on Non-Critical String Theory

    E.J. Martinec, The Annular Report on Noncritical String Theory , arXiv:hep-th/0305148

    work page internal anchor Pith review Pith/arXiv arXiv

Showing first 80 references.