Effective gravitational couplings of four-dimensional N = 2 supersymmetric gauge theories

A bstract The low energy effective couplings of a four-dimensional N = 2 supersymmetric gauge theory to topological invariants of the background gravitational field are described by two functions A and B . These two functions play an important role in the study of topo- logically twisted four-dimensional N = 2 supersymmetric gauge theories and in the computation of central charges of N = 2 superconformal theories. In this paper, we compute A and B from the partition function in the Ω-background for SU(2) gauge theories. Our results not only confirm the predicted expressions of the effective gravitational couplings, but also give the previously undetermined overall multiplicative factors. We also analyze A and B for the SU( N ) super-Yang-Mills theory, and confirm all the previous predictions.