Theory HEP Seminar

3d & 5d holomorphic blocks for SUSY gauge theories

Fabrizio Nieri

University of Surrey

In recent years, due to the method of supersymmetric localization, many exact results have been achieved in the study of supersymmetric gauge theories on compact spaces of various dimension and topology, discovering surpraising structures. For example, it is becoming clear that partition functions of a large variety of such theories can be described in terms of fundamental building blocks and gluing rules. One of the best understood case can be found in 3d N=2 theories defined on manifolds admitting a Heegaard decomposition in solid tori, where partition functions can be given by fusing 3d holomorphic blocks by elements in SL(2,Z). This was explicitly checked for theories on S2xS1 and S3, and I will show this is indeed the case for more general manifolds such as lens spaces. Recently, holomorphic blocks have been introduced also for 5d N=1 theories, and I will review how partition functions on S5, S4xS1 and Y^pq spaces can be built out of them.