Holomorphic Blocks in Three Dimensions

Christopher Beem, Tudor Dimofte, Sara Pasquetti

Research output: Contribution to journalArticlepeer-review

Abstract

We decompose sphere partition functions and indices of three-dimensional N=2 gauge theories into a sum of products involving a universal set of "holomorphic blocks". The blocks count BPS states and are in one-to-one 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 three-dimensional mirror symmetry. The blocks also have interesting dual interpretations. For theories arising from the compactification of the six-dimensional (2,0) theory on a three-manifold M, the blocks belong to a basis of wavefunctions in analytically continued Chern-Simons theory on M. For theories engineered on branes in Calabi-Yau geometries, the blocks offer a non-perturbative perspective on open topological string partition functions.
Original languageEnglish
Article number177
Number of pages125
Journal Journal of High Energy Physics
Volume2014
Issue number12
DOIs
Publication statusPublished - 30 Dec 2014

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