BPS States in the Duality Web of the Omega deformation

TL;DR

This paper explores the duality web of Omega-deformed six-dimensional gauge theories, connecting them to a new reciprocal gauge theory and analyzing BPS states through various dualities, revealing novel stable states.

Contribution

It introduces the reciprocal gauge theory derived from Omega-deformed (2,0) theories and studies BPS states across dualities, providing new insights into their stability and properties.

Findings

Identification of the reciprocal gauge theory with Liouville-like properties

Realization of BPS states in different duality frames

Discovery of perturbatively stable states in the reciprocal frame

Abstract

In this note, we study different limits of an Omega-deformed (2,0) six-dimensional gauge theory realized in a M-theory fluxtrap background. Via a chain of dualities, we connect the Omega-deformed SYM to a new four-dimensional gauge theory which we refer to as the reciprocal gauge theory. This theory has several properties in common with Liouville field theory, such as its gauge coupling b^2 =\epsilon_2 / \epsilon_1, and its behavior under S-duality. Finally, we realize the BPS states on the SYM side of the AGT correspondence and follow them along the chain of dualities. In the fluxtrap frame, we are dealing with two distinct types of states localized in different radial positions, while in the reciprocal frame, we find single states carrying both charges localized in one place which appear to be perturbatively stable. Our microscopic picture of the small-b limit exhibits semiclassically BPS bound states, which are not visible at the level of the partition function.