Partition Functions of N=(2,2) Gauge Theories on S2 and Vortices

Benini, Francesco; Cremonesi, Stefano

Abstract

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2)N=(2,2) R-symmetric theory of vector and chiral multiplets on S2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet–Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. For applications, we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions.

Citation

Benini, F., & Cremonesi, S. (2014). Partition Functions of N=(2,2) Gauge Theories on S2 and Vortices. Communications in Mathematical Physics, 334(3), 1483-1527. https://doi.org/10.1007/s00220-014-2112-z

• Journal Article Type: Article
• Acceptance Date: Dec 16, 2013
• Online Publication Date: Jul 17, 2014
• Publication Date: Jul 17, 2014
• Deposit Date: Feb 2, 2017
• Publicly Available Date: Sep 15, 2017
• Journal: Communications in Mathematical Physics
• Print ISSN: 0010-3616
• Electronic ISSN: 1432-0916
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 334
• Issue: 3
• Pages: 1483-1527
• DOI: https://doi.org/10.1007/s00220-014-2112-z
• Public URL: https://durham-repository.worktribe.com/output/1366128
• Related Public URLs: https://arxiv.org/abs/1206.2356