M5-branes, toric diagrams and gauge theory duality

TL;DR

This paper investigates a duality between two five-dimensional quiver gauge theories by comparing their Seiberg-Witten curves and Nekrasov partition functions, revealing a map between their parameters and implications for mathematical identities and 2D SCFTs.

Contribution

It establishes a detailed duality map between two classes of 5D gauge theories and connects this duality to mathematical identities and 2D superconformal field theories via the AGTW conjecture.

Findings

Derived a parameter map between dual gauge theories.

Connected the duality to identities in mathematical physics.

Linked 5D gauge theories to 2D SCFT correlation functions.

Abstract

In this article we explore the duality between the low energy effective theory of five-dimensional N=1 SU(N)^{M-1} and SU(M)^{N-1} linear quiver gauge theories compactified on S^1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.