Alpha- and Omega-Deformations from fluxes in M-Theory

TL;DR

This paper introduces a new family of deformations for N=2 gauge theories derived from M-theory flux backgrounds, including the Omega- and a novel Alpha-deformation related by S-duality, analyzed via Lagrangian and M-theory approaches.

Contribution

It presents the first derivation of an Alpha-deformation as an S-dual to the Omega-deformation from M-theory flux backgrounds, with explicit Lagrangian and M-theory descriptions.

Findings

Constructed a non-Abelian, UV-complete Lagrangian for the deformed theories.

Demonstrated the strong coupling lift to M-theory via M5-brane equations.

Identified the Alpha-deformation as S-dual to the Omega-deformation.

Abstract

We discuss an SL(2,R) family of deformed N=2 four-dimensional gauge theories which we derive from a flux background in M-theory. In addition to the Omega-deformation this family includes a new deformation, which we call the Alpha-deformation, which can be viewed as an S-dual to the Omega-deformation. We study these gauge theories in two ways: by constructing a non-Abelian (but UV-complete) Lagrangian, and by their strong coupling lift to M-theory where their low-energy dynamics can be determined by examining the equation of motion of a single M5-brane wrapped on a Riemann surface.