Abstract
Significant progresses have been made recently in understanding the spectral form factor of Jackiw-Teitelboim gravity, particularly at late times where non-perturbative effects are expected to play a dominant role. By focusing on a peculiar regime of large time and fixed temperature, called τ-scaling limit, it was found that it is possible to analytically investigate the late-time plateau directly through the gravitational genus expansion. We extend this analysis to the supersymmetric \( \mathcal{N} \) = 1 generalization of the bosonic theory, revealing an interesting structure. First, we notice that in the τ-scaling limit the perturbative sum over genera truncates after a single term, which solely accounts for the ramp behaviour. Instead a non-perturbative completion, responsible for the plateau, is encoded into an exact formula coming from the properties of the chiral gaussian ensemble, governing the spectral properties of the supersymmetric theory. We are able to recover the non-perturbative contributions by slightly deforming the genus of the involved surfaces and using resurgence theory. We derive a closed-form analytical expression for the late-time plateau and a trans-series expansion that captures the ramp-plateau transition.
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References
A. Almheiri et al., Replica Wormholes and the Entropy of Hawking Radiation, JHEP 05 (2020) 013 [arXiv:1911.12333] [INSPIRE].
G. Penington, S.H. Shenker, D. Stanford and Z. Yang, Replica wormholes and the black hole interior, JHEP 03 (2022) 205 [arXiv:1911.11977] [INSPIRE].
A. Blommaert, T.G. Mertens and H. Verschelde, Clocks and Rods in Jackiw-Teitelboim Quantum Gravity, JHEP 09 (2019) 060 [arXiv:1902.11194] [INSPIRE].
P. Saad, Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity, arXiv:1910.10311 [INSPIRE].
A. Blommaert, Dissecting the ensemble in JT gravity, JHEP 09 (2022) 075 [arXiv:2006.13971] [INSPIRE].
L. Leviandier, M. Lombardi, R. Jost and J.P. Pique, Fourier Transform: A Tool to Measure Statistical Level Properties in Very Complex Spectra, Phys. Rev. Lett. 56 (1986) 2449 [INSPIRE].
J.M. Maldacena, Eternal black holes in anti-de Sitter, JHEP 04 (2003) 021 [hep-th/0106112] [INSPIRE].
J.S. Cotler et al., Black Holes and Random Matrices, JHEP 05 (2017) 118 [Erratum ibid. 09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett. 70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP 05 (2018) 183 [arXiv:1711.08467] [INSPIRE].
Y.-Z. You, A.W.W. Ludwig and C. Xu, Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States, Phys. Rev. B 95 (2017) 115150 [arXiv:1602.06964] [INSPIRE].
A.M. García-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev. D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].
O. Bohigas, M.J. Giannoni and C. Schmit, Characterization of chaotic quantum spectra and universality of level fluctuation laws, Phys. Rev. Lett. 52 (1984) 1 [INSPIRE].
R. Jackiw, Lower Dimensional Gravity, Nucl. Phys. B 252 (1985) 343 [INSPIRE].
C. Teitelboim, Gravitation and Hamiltonian Structure in Two Space-Time Dimensions, Phys. Lett. B 126 (1983) 41 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
C.V. Johnson, Explorations of nonperturbative Jackiw-Teitelboim gravity and supergravity, Phys. Rev. D 103 (2021) 046013 [arXiv:2006.10959] [INSPIRE].
P. Saad, D. Stanford, Z. Yang and S. Yao, A convergent genus expansion for the plateau, arXiv:2210.11565 [INSPIRE].
A. Blommaert, J. Kruthoff and S. Yao, An integrable road to a perturbative plateau, JHEP 04 (2023) 048 [arXiv:2208.13795] [INSPIRE].
K. Okuyama and K. Sakai, Spectral form factor in the τ-scaling limit, JHEP 04 (2023) 123 [arXiv:2301.04773] [INSPIRE].
D. Stanford and E. Witten, JT gravity and the ensembles of random matrix theory, Adv. Theor. Math. Phys. 24 (2020) 1475 [arXiv:1907.03363] [INSPIRE].
G. Akemann, V. Gorski and M. Kieburg, Consecutive level spacings in the chiral Gaussian unitary ensemble: from the hard and soft edge to the bulk, J. Phys. A 55 (2022) 194002 [arXiv:2112.12447] [INSPIRE].
J. Écalle, Les fonctions résurgentes. Tome I, Université de Paris-Sud Département de Mathématique, Orsay, (1981).
P. Gregori and R. Schiappa, From minimal strings towards Jackiw-Teitelboim gravity: on their resurgence, resonance, and black holes, Class. Quant. Grav. 41 (2024) 115001 [arXiv:2108.11409] [INSPIRE].
B. Eynard et al., Resurgent Asymptotics of Jackiw-Teitelboim Gravity and the Nonperturbative Topological Recursion, arXiv:2305.16940 [INSPIRE].
R. Schiappa, M. Schwick and N. Tamarin, All the D-Branes of Resurgence, arXiv:2301.05214 [INSPIRE].
B. Eynard and N. Orantin, Invariants of algebraic curves and topological expansion, Commun. Num. Theor. Phys. 1 (2007) 347 [math-ph/0702045] [INSPIRE].
C. Kozçaz, T. Sulejmanpasic, Y. Tanizaki and M. Ünsal, Cheshire Cat resurgence, Self-resurgence and Quasi-Exact Solvable Systems, Commun. Math. Phys. 364 (2018) 835 [arXiv:1609.06198] [INSPIRE].
D. Dorigoni and P. Glass, The grin of Cheshire cat resurgence from supersymmetric localization, SciPost Phys. 4 (2018) 012 [arXiv:1711.04802] [INSPIRE].
D. Dorigoni and P. Glass, Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D \( \mathcal{N} \) = 2 field theories, JHEP 12 (2019) 085 [arXiv:1909.05262] [INSPIRE].
T. Fujimori and P. Glass, Resurgence in 2-dimensional Yang-Mills and a genus-altering deformation, PTEP 2023 (2023) 053B03 [arXiv:2212.11988] [INSPIRE].
K. Okuyama and K. Sakai, ’t Hooft expansion of multi-boundary correlators in 2D topological gravity, PTEP 2021 (2021) 083B03 [arXiv:2101.10584] [INSPIRE].
M. Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, Invent. Math. 167 (2006) 179 [INSPIRE].
M. Mirzakhani, Weil-Petersson volumes and intersection theory on the moduli space of curves, J. Am. Math. Soc. 20 (2007) 1 [INSPIRE].
P. Norbury, Enumerative geometry via the moduli space of super Riemann surfaces, arXiv:2005.04378 [INSPIRE].
T. Weber, F. Haneder, K. Richter and J.D. Urbina, Constraining Weil-Petersson volumes by universal random matrix correlations in low-dimensional quantum gravity, J. Phys. A 56 (2023) 205206 [arXiv:2208.13802] [INSPIRE].
C.V. Johnson, Nonperturbative Jackiw-Teitelboim gravity, Phys. Rev. D 101 (2020) 106023 [arXiv:1912.03637] [INSPIRE].
Q.-M. Luo, Apostol-euler polynomials of higher order and gaussian hypergeometric functions, Taiwanese J. Math. 10 (2006) 917.
G.J. Turiaci and E. Witten, \( \mathcal{N} \) = 2 JT supergravity and matrix models, JHEP 12 (2023) 003 [arXiv:2305.19438] [INSPIRE].
C.V. Johnson, A Non-Perturbative Random Matrix Model of \( \mathcal{N} \) = 2 JT Supergravity, arXiv:2306.10139 [INSPIRE].
K. Okuyama and K. Sakai, JT supergravity and Brezin-Gross-Witten tau-function, JHEP 10 (2020) 160 [arXiv:2007.09606] [INSPIRE].
K. Okuyama and K. Sakai, JT gravity, KdV equations and macroscopic loop operators, JHEP 01 (2020) 156 [arXiv:1911.01659] [INSPIRE].
K. Okuyama and K. Sakai, Multi-boundary correlators in JT gravity, JHEP 08 (2020) 126 [arXiv:2004.07555] [INSPIRE].
T.R. Morris, 2-D quantum gravity, multicritical matter and complex matrices, FERMILAB-PUB-90-136-T (1990) [INSPIRE].
S. Dalley, C.V. Johnson and T.R. Morris, Multicritical complex matrix models and nonperturbative 2-D quantum gravity, Nucl. Phys. B 368 (1992) 625 [INSPIRE].
S. Dalley, C.V. Johnson, T.R. Morris and A. Watterstam, Unitary matrix models and 2-D quantum gravity, Mod. Phys. Lett. A 7 (1992) 2753 [hep-th/9206060] [INSPIRE].
I.R. Klebanov, J.M. Maldacena and N. Seiberg, Unitary and complex matrix models as 1-d type 0 strings, Commun. Math. Phys. 252 (2004) 275 [hep-th/0309168] [INSPIRE].
E. Brezin and A. Zee, Universality of the correlations between eigenvalues of large random matrices, Nucl. Phys. B 402 (1993) 613 [INSPIRE].
F.J. Dyson, Statistical theory of the energy levels of complex systems. I, J. Math. Phys. 3 (1962) 140 [INSPIRE].
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Griguolo, L., Papalini, J., Russo, L. et al. The resurgence of the plateau in supersymmetric \( \mathcal{N} \) = 1 Jackiw-Teitelboim gravity. J. High Energ. Phys. 2024, 168 (2024). https://doi.org/10.1007/JHEP06(2024)168
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DOI: https://doi.org/10.1007/JHEP06(2024)168