On RG flow of τ _RR for supersymmetric field theories in three-dimensions

The coefficient τ _RR 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 τ _RR 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 τ _RR under an RG flow by adding superpotentials to the theories. While the τ _RR decreases for the gauge theories, we find an N=2 Wess-Zumino model whose τ _RR increases along the RG flow. Since τ _RR is proportional to the coefficient C _T of the two-point correlation function of the stress-energy tensors for N=2 superconformal field theories, this rules out the possibility of C _T being a measure of the degrees of freedom which monotonically decreases along RG flows in three-dimensions.