Resurgence, Painlevé equations and conformal blocks
Abstract
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 interrelations; 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 nonperturbative sectors of associated spectral problems, via the Bethegauge and Painlevégauge 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.
 Authors:

 Univ. of Connecticut, Storrs, CT (United States)
 Publication Date:
 Research Org.:
 Univ. of Connecticut, Storrs, CT (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), High Energy Physics (HEP)
 OSTI Identifier:
 1594816
 Grant/Contract Number:
 SC0010339; PHY1125915
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physics. A, Mathematical and Theoretical
 Additional Journal Information:
 Journal Volume: 52; Journal Issue: 46; Journal ID: ISSN 17518113
 Publisher:
 IOP Publishing
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; resurgence; Painlevé systems; conformal blocks
Citation Formats
Dunne, Gerald V. Resurgence, Painlevé equations and conformal blocks. United States: N. p., 2019.
Web. doi:10.1088/17518121/ab3142.
Dunne, Gerald V. Resurgence, Painlevé equations and conformal blocks. United States. https://doi.org/10.1088/17518121/ab3142
Dunne, Gerald V. Mon .
"Resurgence, Painlevé equations and conformal blocks". United States. https://doi.org/10.1088/17518121/ab3142. https://www.osti.gov/servlets/purl/1594816.
@article{osti_1594816,
title = {Resurgence, Painlevé equations and conformal blocks},
author = {Dunne, Gerald V.},
abstractNote = {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 interrelations; 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 nonperturbative sectors of associated spectral problems, via the Bethegauge and Painlevégauge 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.},
doi = {10.1088/17518121/ab3142},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 46,
volume = 52,
place = {United States},
year = {2019},
month = {10}
}
Web of Science
Figures / Tables:
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The sixth Painlevé transcendent and uniformization of algebraic curves
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Monodromy dependence and connection formulae for isomonodromic tau functions
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Bands and gaps in Nekrasov partition function
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 Gorsky, A.; Milekhin, A.; Sopenko, N.
 arXiv
Random Matrix Theory and Entanglement in Quantum Spin Chains
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 Keating, J. P.; Mezzadri, F.
 arXiv