Exact WKB methods in SU(2) Nf = 1

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.

Wigner Functions versus WKB-Methods

We consider the Cauchy-problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods, leading to ”multi-valued” solutions of Hamilton-Jacobi equations. Using Wigner measures we present an...

WKB-Methods in Multivalued Geometrical Optics

We consider the Cauchy problem for a class of scalar linear dispersive equations with rapidly oscillating initial data. The problem of the high-frequency asymptotics of such models is reviewed, in particular we highlight the difficulties in crossing caustics when using (time-dependent) WKB-methods. Using Wigner measures we present an alternative approach to such asymptotic problems. We first di...

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

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...