1302.6095 (Min-xin Huang)

Modular Anomaly from Holomorphic Anomaly in Mass Deformed N=2
Superconformal Field Theories    [PDF]

Min-xin Huang

We study the instanton partition functions of two well-known superconformal field theories, namely the SU(2) N=2 gauge theories with an adjoint hypermultiplet and with Nf=4 fundamental hypermultiplets, with mass deformations. It has been known that there is a modular anomaly equation for the instanton partition functions in terms of the bare coupling constants of the theories. On the other hand, the holomorphic anomaly equation in terms of the renormalized gauge coupling constants has been derived from topological string theory. We elucidate the relation between modular anomaly and holomorphic anomaly in the two theories. The quasi-modularity appearing in the expansion of the instanton partition functions can be explained by a SL(2,Z) duality transformation of Coulomb modulus parameter.

View original: http://arxiv.org/abs/1302.6095