Resurgence, Painleve Equations and Conformal Blocks

Abstract

We discuss some physical consequences of the resurgent structure of Painleve equations and their related conformal block expansions. The resurgent structure of Painleve 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 Painleve-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 Painleve VI, Painleve III and Painleve V, respectively.

32 pp

References in corpus (15)

• A Primer on Resurgent Transseries and Their Asymptotics
• Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
• TBA equations and resurgent Quantum Mechanics
• Classical irregular block, N=2 pure gauge theory and Mathieu equation
• Poles of Integrale Tritronquee and Anharmonic Oscillators. Asymptotic localization from WKB analysis
• Holonomy of the Ising model form factors
• Non-Perturbative Quantum Geometry II
• On determinant representation and integrability of Nekrasov functions
• Argyres-Douglas theories, Painlevé II and quantum mechanics
• Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
• Transmutation of a Trans-series: The Gross-Witten-Wadia Phase Transition
• Complex saddles in the Gross-Witten-Wadia matrix model
• Random Matrix Theory and the Sixth Painlevé Equation
• Bands and gaps in Nekrasov partition function
• Leading corrections to the scaling function on the diagonal for the two-dimensional Ising model

Cited by in corpus (8)

• Delayed Deconfinement and the Hawking-Page Transition
• A slow review of the AGT correspondence
• Confluent conformal blocks and the Teukolsky master equation
• Instantons to the people: the power of one-form symmetries
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Expansions for semiclassical conformal blocks
• Two-point functions at arbitrary genus and its resurgence structure in a matrix model for 2D type IIA superstrings
• Resurgent Trans-Series for Generalized Hastings-McLeod Solutions