Charges of Monopole Operators in Chern-Simons Yang-Mills Theory

TL;DR

This paper calculates the exact non-abelian R-charges of monopole operators in N=3 supersymmetric Chern-Simons Yang-Mills theories, including ABJM, revealing their role in spectrum matching and supersymmetry enhancement.

Contribution

It provides a one-loop exact computation of monopole R-charges in N=3 theories, applicable at all couplings, and demonstrates the existence of monopole operators with zero scaling dimension in ABJM.

Findings

Monopole operators have quantized SU(2)_R charges related to Wess-Zumino terms.

In ABJM theory, the relevant Wess-Zumino coefficient h=0, indicating monopole operators with zero dimension.

Existence of monopole operators as singlets under all global symmetries supports spectrum matching with supergravity.

Abstract

We calculate the non-abelian R-charges of BPS monopole operators in three-dimensional gauge theories with N=3 supersymmetry. This class of models includes ABJM theory, the proposed gauge theory dual of M-theory on AdS_4 x S^7/Z_k, as a special case. In the UV limit of the N=3 theories the Yang-Mills coupling becomes weak and the monopole operators are described by classical backgrounds. This allows us to find their SU(2)_R charges in a one-loop computation which by virtue of the non-renormalization of non-abelian R-charges yields the exact result for any value of the coupling. The spectrum of SU(2)_R charges is found by quantizing the SU(2)/U(1) collective coordinate of the BPS background, whose dynamics is that of a charged particle on a sphere with a Wess-Zumino term representing a magnetic monopole at its center. If the Wess-Zumino coefficient is h, then the smallest possible SU(2)_R representation for BPS monopole operators has spin |h|/2. We find, in agreement with earlier proposals, that h is proportional to the sum of the U(1)_R charges of all the fermion fields weighted by the effective monopole charges determined by their gauge representations. The field content of ABJM theory is such that h=0. This proves for any Chern-Simons level k the existence of monopole operators which are singlets under all global symmetries and have vanishing scaling dimensions. These operators are essential for matching the spectrum of the ABJM theory with supergravity and for the supersymmetry enhancement to N=8.