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

Benini, Francesco; Cremonesi, Stefano

doi:10.1007/s00220-014-2112-z

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

Benini, Francesco; Cremonesi, Stefano

Authors

Francesco Benini

Dr Stefano Cremonesi stefano.cremonesi@durham.ac.uk
Associate Professor

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
Related Public URLs	https://arxiv.org/abs/1206.2356