Quantum Curves, Resurgence and Exact WKB

WKB and Resurgence in the Mathieu Equation

In this paper, based on lectures by the authors at the May 2015 workshop Resurgence, Physics and Numbers, at the Centro di Ricerca Matematica Ennio De Giorgio of the Scuola Normale Superiore in Pisa, we explain the origin of resurgent trans-series in the Mathieu equation spectral problem, using uniform WKB and all-orders (exact) WKB. Exact quantization conditions naturally arise, and their expa...

QHJ, WKB and exact quantisation

We present a simple derivation of the WKB quantisation condition using the quantum Hamilton-Jacobi formalism and propose an exact quantisation condition within this formalism for integrable models in higher dimensions.

Pure N = 2 super Yang - Mills and exact WKB

We apply exact WKB methods to the study of the partition function of pure N = 2 i-deformed gauge theory in four dimensions in the context of the 2d/4d correspondence. We study the partition function at leading order in 2/ 1 (i.e. at large central charge) and in an expansion in 1. We find corrections of the form ∼ exp[− periods 1 ] to this expansion. We attribute these to the exchange of the ord...

On the exact WKB analysis of microdifferential operators of WKB type ∗ Takashi AOKI

WKB-type Approximation to Noncommutative Quantum Cosmology

In this work, we develop and apply the WKB approximation to several examples of noncommutative quantum cosmology, obtaining the time evolution of the noncommutative universe, this is done starting from a noncommutative quantum formulation of cosmology where the noncommutativity is introduced by a deformation on the minisuperspace variables. This procedure gives a straightforward algorithm to in...