Resurgence, Painlevé equations and conformal blocks

Dunne, Gerald V.

doi:10.1088/1751-8121/ab3142

Title: Resurgence, Painlevé equations and conformal blocks

Journal Article · 21 October 2019 · Journal of Physics. A, Mathematical and Theoretical

DOI: https://doi.org/10.1088/1751-8121/ab3142 · OSTI ID:1594816

^[1]

Univ. of Connecticut, Storrs, CT (United States); UConn

We discuss some physical consequences of the resurgent structure of Painlevé equations and their related conformal block expansions. Here, the resurgent structure of Painlevé equations is particularly transparent when expressed in terms of physical conformal block expansions of the associated tau functions. Resurgence produces an intricate network of inter-relations; some between expansions around different critical points, others between expansions around different instanton sectors of the expansions about the same critical point, and others between different non-perturbative sectors of associated spectral problems, via the Bethe-gauge and Painlevé-gauge correspondences. Resurgence relations exist both for convergent and divergent expansions, and can be interpreted in terms of the physics of phase transitions. These general features are illustrated with three physical examples: correlators of the 2d Ising model, the partition function of the Gross–Witten–Wadia matrix model, and the full counting statistics of one dimensional fermions, associated with Painlevé VI, Painlevé III and Painlevé V, respectively.

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Research Organization:: Univ. of Connecticut, Storrs, CT (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

Grant/Contract Number:: SC0010339

OSTI ID:: 1594816

Journal Information:: Journal of Physics. A, Mathematical and Theoretical, Journal Name: Journal of Physics. A, Mathematical and Theoretical Journal Issue: 46 Vol. 52; ISSN 1751-8113

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

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Studies on holonomic quantum fields, XVI. Density matrix of impenetrable bose gas Jimbo, Michio; Miwa, Tetsuji; Mōri, Yasuko Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 55, Issue 9 https://doi.org/10.3792/pjaa.55.317	journal	January 1979
Polynomial Hamiltonians associated with Painlevé equations, II. Differential equations satisfied by polynomial Hamiltonians Okamoto, Kazuo Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 56, Issue 8 https://doi.org/10.3792/pjaa.56.367	journal	January 1980
Studies on holonomic quantum fields, XVII Jimbo, Michio; Miwa, Tetsuji Proceedings of the Japan Academy, Series A, Mathematical Sciences, Vol. 56, Issue 9 https://doi.org/10.3792/pjaa.56.405	journal	January 1980
The Two-Dimensional Ising Model McCoy, Barry M.; Wu, Tai Tsun Harvard University Press https://doi.org/10.4159/harvard.9780674180758	book	December 1973
Seiberg-Witten Prepotential from Instanton Counting Nekrasov, Nikita A. Advances in Theoretical and Mathematical Physics, Vol. 7, Issue 5 https://doi.org/10.4310/ATMP.2003.v7.n5.a4	journal	January 2003
Nonperturbative effects and nonperturbative definitions in matrix models and topological strings Marino, Marcos arXiv https://doi.org/10.48550/arxiv.0805.3033	text	January 2008
Liouville Correlation Functions from Four-dimensional Gauge Theories Alday, Luis F.; Gaiotto, Davide; Tachikawa, Yuji arXiv https://doi.org/10.48550/arxiv.0906.3219	text	January 2009
Wall-crossing, Hitchin Systems, and the WKB Approximation Gaiotto, Davide; Moore, Gregory W.; Neitzke, Andrew arXiv https://doi.org/10.48550/arxiv.0907.3987	preprint	January 2009
Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis Masoero, Davide; De Benedetti, Vera arXiv https://doi.org/10.48550/arxiv.1002.1042	text	January 2010
The sixth Painleve transcendent and uniformization of algebraic curves Brezhnev, Yurii V. arXiv https://doi.org/10.48550/arxiv.1011.1645	text	January 2010
On combinatorial expansion of the conformal blocks arising from AGT conjecture Alba, V. A.; Fateev, V. A.; Litvinov, A. V. arXiv https://doi.org/10.48550/arxiv.1012.1312	text	January 2010
A Review on The Sixth Painleve' Equation Guzzetti, Davide arXiv https://doi.org/10.48550/arxiv.1210.0311	text	January 2012
The toroidal block and the genus expansion Kashani-Poor, Amir-Kian; Troost, Jan arXiv https://doi.org/10.48550/arxiv.1212.0722	text	January 2012
Uniform WKB, Multi-instantons, and Resurgent Trans-Series Dunne, Gerald V.; Unsal, Mithat arXiv https://doi.org/10.48550/arxiv.1401.5202	text	January 2014
Isomonodromic tau-functions from Liouville conformal blocks Iorgov, N.; Lisovyy, O.; Teschner, J. arXiv https://doi.org/10.48550/arxiv.1401.6104	text	January 2014
Non-Perturbative Quantum Geometry II Krefl, Daniel arXiv https://doi.org/10.48550/arxiv.1410.7116	text	January 2014
Classical limit of irregular blocks and Mathieu functions Piatek, Marcin; Pietrykowski, Artur R. arXiv https://doi.org/10.48550/arxiv.1509.08164	text	January 2015
On Information Loss in AdS$_3$/CFT$_2$ Fitzpatrick, A. Liam; Kaplan, Jared; Li, Daliang arXiv https://doi.org/10.48550/arxiv.1603.08925	preprint	January 2016
The anisotropic Ising correlations as elliptic integrals: duality and differential equations McCoy, B. M.; Maillard, J-M. arXiv https://doi.org/10.48550/arxiv.1606.08796	text	January 2016
Holomorphic Anomaly and Quantum Mechanics Codesido, Santiago; Marino, Marcos arXiv https://doi.org/10.48550/arxiv.1612.07687	text	January 2016
Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations Basar, Gokce; Dunne, Gerald V.; Unsal, Mithat arXiv https://doi.org/10.48550/arxiv.1701.06572	text	January 2017
Bands and gaps in Nekrasov partition function Gorsky, A.; Milekhin, A.; Sopenko, N. arXiv https://doi.org/10.48550/arxiv.1712.02936	text	January 2017
A Primer on Resurgent Transseries and Their Asymptotics Aniceto, Inês; Başar, Gökçe; Schiappa, Ricardo arXiv https://doi.org/10.48550/arxiv.1802.10441	text	January 2018
TBA equations and resurgent Quantum Mechanics Ito, Katsushi; Mariño, Marcos; Shu, Hongfei arXiv https://doi.org/10.48550/arxiv.1811.04812	text	January 2018
The large-N expansion of unitary-matrix models Rossi, Paolo; Campostrini, Massimo; Vicari, Ettore arXiv https://doi.org/10.48550/arxiv.hep-lat/9609003	text	January 1996

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