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.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics