D-brane Charges in Gravitational Duals of 2+1 Dimensional Gauge Theories and Duality Cascades

TL;DR

This paper analyzes D-brane charges in string theory duals of 2+1 dimensional gauge theories, generalizing known duals, clarifying charge shifts, and proposing possible duality cascades in N=3 theories.

Contribution

It extends gravitational duals to arbitrary couplings, clarifies IR charge shifts, and suggests duality cascades in N=3 supersymmetric gauge theories.

Findings

Generalized duals to arbitrary gauge couplings.

Identified a 1/2 shift in the IR B-field charge.

Proposed duality cascades similar to Klebanov-Strassler.

Abstract

We perform a systematic analysis of the D-brane charges associated with string theory realizations of d=3 gauge theories, focusing on the examples of the N=4 supersymmetric U(N)xU(N+M) Yang-Mills theory and the N=3 supersymmetric U(N)xU(N+M) Yang-Mills-Chern-Simons theory. We use both the brane construction of these theories and their dual string theory backgrounds in the supergravity approximation. In the N=4 case we generalize the previously known gravitational duals to arbitrary values of the gauge couplings, and present a precise mapping between the gravity and field theory parameters. In the N=3 case, which (for some values of N and M) flows to an N=6 supersymmetric Chern-Simons-matter theory in the IR, we argue that the careful analysis of the charges leads to a shift in the value of the B-field in the IR solution by 1/2, in units where its periodicity is one, compared to previous claims. We also suggest that the N=3 theories may exhibit, for some values of N and M, duality cascades similar to those of the Klebanov-Strassler theory.