Non-Perturbative Quantum Geometry III

TL;DR

This paper investigates non-perturbative quantum geometry derived from refined topological string theory on toric Calabi-Yau manifolds, revealing Stokes phenomena and band splitting, with numerical evidence connecting to supersymmetric gauge theories.

Contribution

It introduces a formalism for exact quantization applicable at points with massless hypermultiplets, demonstrating non-perturbative effects in quantum geometry and gauge theories.

Findings

Quantum differential exhibits Stokes phenomena.

Non-perturbative band splitting observed.

Quantum geometry reproduces gauge theory corrections.

Abstract

The Nekrasov-Shatashvili limit of the refined topological string on toric Calabi-Yau manifolds and the resulting quantum geometry is studied from a non-perturbative perspective. The quantum differential and thus the quantum periods exhibit Stokes phenomena over the combined string coupling and quantized Kaehler moduli space. We outline that the underlying formalism of exact quantization is generally applicable to points in moduli space featuring massless hypermultiplets, leading to non-perturbative band splitting. Our prime example is local P1xP1 near a conifold point in moduli space. In particular, we will present numerical evidence that in a Stokes chamber of interest the string based quantum geometry reproduces the non-perturbative corrections for the Nekrasov-Shatashvili limit of 4d supersymmetric SU(2) gauge theory at strong coupling found in the previous part of this series. A preliminary discussion of local P2 near the conifold point in moduli space is also provided.