Refined Topological Vertex and Duality of Gauge Theories in Generic Omega Backgrounds

TL;DR

This paper computes refined topological string partition functions for 5D supersymmetric gauge theories in generic Omega backgrounds, demonstrating dualities between different quiver gauge theories and analyzing moduli relations.

Contribution

It explicitly proves the duality between $SU(N)^{M-1}$ and $SU(M)^{N-1}$ gauge theories in generic Omega backgrounds, extending previous results beyond self-dual cases.

Findings

Duality holds between the gauge theories even in generic Omega backgrounds.

Relations between string and gauge moduli are deformed from the self-dual case.

Duality maps preserving the Omega background ratio remain unchanged from the self-dual case.

Abstract

The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds. Based on the slicing independence conjecture of refined topological string partition functions, it is demonstrated explicitly that the duality exists between $SU(N)^{M-1}$ and $SU(M)^{N-1}$ supersymmetric linear quiver gauge theories, even in generic Omega backgrounds. It is found that the relations between string moduli and gauge moduli are deformed from the self-dual case. However if the duality map which preserves the ratio of the Omega background parameters q and t, is considered, duality maps of the gauge moduli are not changed from the self-dual case.