Three-Dimensional Gauge Dynamics from Brane Configurations with (p,q)-Fivebrane

TL;DR

This work investigates three-dimensional gauge dynamics realized on type IIB brane configurations that descend from tilted M5-branes in M-theory, focusing on (p,q)-fivebranes and the resulting Maxwell–Chern–Simons systems. By deriving axion-induced CS terms and exploiting SL$(2,\mathbb{Z})$ dualities and brane moves, the authors classify abelian and nonabelian 3D theories, analyze their mirrors, and elucidate the vacuum structure of CS theories via brane pictures. They demonstrate explicit abelian theories with $N_f$ flavors, their magnetic duals, and reveal how discrete CS levels $\kappa=-\frac{p}{q}$ yield $p$-fold vacuum degeneracy tied to M2-brane positions, with brane creation providing additional dual constructions. The results establish a geometric, string-theoretic framework for dualities and vacua in 3D CS theories, with implications for both high-energy theory and potential condensed-matter applications.

Abstract

We study three-dimensional gauge dynamics by using type IIB superstring brane configurations, which can be obtained from the M-theory configuration of M2-branes stretched between two M5-branes with relative angles. Our construction of brane configurations includes (p,q)5-brane and gives a systematic classification of possible three-dimensional gauge theories. The explicit identification of gauge theories are made and their mirror symmetry is discussed. As a new feature, our theories include interesting Maxwell-Chern-Simons system whose vacuum structure is also examined in detail, obtaining results consistent with the brane picture.

Figures (7)

• Figure 1: A $(p,q)$5-brane as an M5-brane wrapping a torus $T^2$$q$ times over $x^2$ and $p$ times over $x^{10}$.
• Figure 2: Induced CS coupling on the D3-brane via the $(p,q)$5-brane, which is a source of an axion field.
• Figure 3: CS theory with $N_f$ matters and its dual theory.
• Figure 4: Duality between MCS theory and SDM and their brane configurations.
• Figure 5: Relation between discrete vacua of CS theory and positions of $M$2-brane in the configuration.