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

Benini, Francesco; Cremonesi, Stefano

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Francesco Benini


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.


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.

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
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