On RG Flow of tauRR for Supersymmetric Field Theories in Three-Dimensions
Abstract
The coefficient tauRR of the two-point function of the superconformal U(1)R currents of N=2 SCFTs in three-dimensions is recently shown to be obtained by differentiating the partition function on a squashed three-sphere with respect to the squashing parameter. With this method, we compute the tauRR for N=2 Wess-Zumino models and SQCD numerically for small number of flavors and analytically in the large number limit. We study the behavior of tauRR under an RG flow by adding superpotentials to the theories. While the tauRR decreases for the gauge theories, we find an N=2 Wess-Zumino model whose tauRR increases along the RG flow. Since tauRR is proportional to the coefficient CT of the two-point correlation function of the stress-energy tensors for N=2 superconformal field theories, this rules out the possibility of CT being a measure of the degrees of freedom which monotonically decreases along RG flows in three-dimensions.
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