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On the exact R charge for N=2 CS theories

A. Amariti

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.

On the exact R charge for N=2 CS theories

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.

Paper Structure

This paper contains 11 sections, 50 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The partition function localized on $S^3$
  3. Field theory result
  4. Exact $R$ in $\mathcal{N}=2$ $SU(N)_k$ CS matter theories
  5. Fundamental and antifundamental representations
  6. Adjoint representation
  7. Symmetric representation
  8. Antisymmetric representation
  9. Conclusions
  10. Conventions on Lie Algebra
  11. Integrals

Figures (1)

  • Figure 1: Weights of the Adjoint of $SU(3)$