Central charges of N=2 superconformal field theories in four dimensions
Alfred D. Shapere, Yuji Tachikawa
TL;DR
This work provides a direct, non-perturbative method to compute the central charges a and c of four-dimensional N=2 SCFTs by relating them to U(1)_R anomalies in a topologically twisted version of the theory. Central to the method is the holomorphic measure factorization on the u-plane, with A and B factors encoding the R-charge shifts and determined from asymptotic and singularity data of Seiberg-Witten curves. The authors apply the framework to a wide array of theories, including N=4 SU(N), SU(N) with 2N flavors, SU(N) Argyres-Douglas points, and F-theory realizations, finding agreement with known results and holographic calculations. They also establish a universal relation between 2a−c and Coulomb-branch operator dimensions and prove bounds on a/c, highlighting deep constraints on the space of N=2 SCFTs and offering a robust tool for exploring both Lagrangian and non-Lagrangian fixed points.
Abstract
We present a general method for computing the central charges a and c of N=2 superconformal field theories corresponding to singular points in the moduli space of N=2 gauge theories. Our method relates a and c to the U(1)_R anomalies of the topologically twisted gauge theory. We evaluate these anomalies by studying the holomorphic dependence of the path integral measure on the moduli. We calculate a and c for superconformal points in a variety of gauge theories, including N=4 SU(N), N=2 pure SU(N) Yang-Mills, and USp(2N) with 1 massless antisymmetric and 4 massive fundamental hypermultiplets. In the latter case, we reproduce the conformal and flavor central charges previously calculated using the gravity duals of these gauge theories. For any SCFT in the class under consideration, we derive a previously conjectured expression for 2a-c in terms of the sum of the dimensions of operators parameterizing the Coulomb branch. Finally, we prove that the ratio a/c is bounded above by 5/4 and below by 1/2.