Localization on three-dimensional manifolds

2016/08/31 by Brian Willett
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8121/aa612f

This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine) which contains 17 Chapters. The complete volume is summarized in arXiv:1608.02952 and it can be downloaded at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf

arxiv created 2016/10/15 · arxiv updated 2017/10/25

Abstract

In this review article we describe the localization of three dimensional N=2 supersymmetric theories on compact manifolds, including the squashed sphere, S³_b, the lens space, S³_b/Z_p, and S² x S¹. We describe how to write supersymmetric actions on these spaces, and then compute the partition functions and other supersymmetric observables by employing the localization argument. We briefly survey some applications of these computations.

Citations

• Localization techniques in quantum field theories