On the exact R charge for N=2 CS theories

TL;DR

This paper verifies the conjecture that the exact R charge in 3D N=2 supersymmetric theories can be obtained by extremizing the S^3 partition function, through explicit calculations in SU(N)_k YM CS theories.

Contribution

It provides a non-trivial check of the extremization principle for R charge by computing it in large k SU(N) theories and comparing with perturbative results.

Findings

The R charge computed matches the perturbative calculations.

The extremization principle holds for various representations.

Supports the conjecture linking partition function extremization to R charge determination.

Abstract

Recently it was argued that the exact R charge for three dimensional N=2 supersymmetric field theories extremizes the partition function localized on S^3. In this paper we check this conjecture by computing the R charge for SU(N)_k YM CS gauge theories at large k for many representations, and we test the agreement with the perturbative results.