On monopole operators in supersymmetric Chern-Simons-matter theories

TL;DR

This paper investigates monopole operators in supersymmetric Chern-Simons-matter theories, resolving apparent duality mismatches by identifying the true chiral monopoles and analyzing their invariance under dualities, with implications for high-spin gravity duals.

Contribution

It identifies the actual chiral monopole operators in supersymmetric theories and demonstrates their invariance under dualities using the supersymmetric index, clarifying monopole mappings in these theories.

Findings

Lowest naive chiral monopole operators are not truly chiral.

The true chiral monopoles depend on colors, flavors, and Chern-Simons level.

Results are invariant under dualities in supersymmetric theories.

Abstract

We discuss monopole operators in $U(N_c)$ Chern-Simons-matter theories in three space-time dimensions. We mention an apparent problem in the matching of such operators in dualities between non-supersymmetric theories, and suggest a possible resolution. A similar apparent problem exists in the mapping of chiral monopole operators in theories with ${\cal N}=2$ supersymmetry. We show that in many theories the lowest naive chiral monopole operator is actually not chiral, and we find the lowest monopole operator that is actually chiral in these theories. It turns out that there are several different forms of this operator, depending on the number of colors, the number of flavours, and the Chern-Simons level. Since we use the supersymmetric index to find the lowest chiral monopoles, our results for these monopoles are guaranteed to be invariant under the dualities in supersymmetric theories. The theories we discuss are believed to be dual in the 't~Hooft large $N_c$ limit to classical high-spin gravity theories. We argue that these theories (supersymmetric or not) should not have classical solutions charged under the $U(1)$ gauge field in the high-spin multiplet.