Seiberg Duality in Chern-Simons Theories with Fundamental and Adjoint Matter

TL;DR

Using type IIB brane constructions, Niarchos extends Seiberg duality to 3d $\mathcal N=2$ Chern-Simons-matter theories that include an adjoint chiral multiplet with a polynomial superpotential $W$. The proposed duality relates an electric $U(N_c)$ theory at level $k$ to a magnetic $U(n N_f + nk - N_c)$ theory with an adjoint $Y$, magnetic mesons $M_i$, and a dual superpotential that reproduces electric deformations; consistency is checked via moduli-space matching and brane dynamics, including an $s$-rule constraint. The work highlights the potential to illuminate IR dynamics in 3d CS-matter systems and raises open questions about dangerously irrelevant operators for large $n$ and possible two-adjoint generalizations requiring further interactions.

Abstract

We explore the dynamics of three-dimensional Chern-Simons gauge theories with N=2 supersymmetry and matter in the fundamental and adjoint representations of the gauge group. Realizing the gauge theories of interest in a setup of threebranes and fivebranes in type IIB string theory we argue for a Seiberg duality that relates Chern-Simons theories with non-trivial superpotentials.

Figures (4)

• Figure 1: A configuration of D3, D5 and NS5-branes that realizes ${\cal N}=2$$U(N_c)$ SQCD in three dimensions with two extra adjoint chiral superfields.
• Figure 2: $k$ D5-branes recombining with $n'$ NS5-branes to give an $(n',k)$ fivebrane bound state.
• Figure 3: The configuration of branes after the reconnection of $k$ D5-branes and $n'$ NS5$'$-branes. The notation $\left[ {3 \atop 7}\right]_\theta$ denotes the fact that the $(n',k)$ brane is rotated in the $(37)$ plane with an angle $\theta$.
• Figure 4: The magnetic configuration of branes for general $n,n'$.