Holomorphic blocks in three dimensions
Abstract
We decompose sphere partition functions and indices of threedimensional = 2 gauge theories into a sum of products involving a universal set of "holomorphic blocks". The blocks count BPS states and are in onetoone correspondence with the theory's massive vacua. We also propose a new, effective technique for calculating the holomorphic blocks, inspired by a reduction to supersymmetric quantum mechanics. The blocks turn out to possess a wealth of surprising properties, such as a Stokes phenomenon that integrates nicely with actions of threedimensional mirror symmetry. The blocks also have interesting dual interpretations. For theories arising from the compactification of the sixdimensional (2, 0) theory on a threemanifold M, the blocks belong to a basis of wavefunctions in analytically continued ChernSimons theory on M. For theories engineered on branes in CalabiYau geometries, the blocks offer a nonperturbative perspective on open topological string partition functions.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2014
 DOI:
 10.1007/JHEP12(2014)177
 arXiv:
 arXiv:1211.1986
 Bibcode:
 2014JHEP...12..177B
 Keywords:

 Supersymmetric gauge theory;
 Supersymmetry and Duality;
 Topological Field Theories;
 High Energy Physics  Theory
 EPrint:
 124 pages, 21 figures. v3: Typos corrected