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Partition functions of N=(2,2) gauge theories on S2 and vortices.

Benini, Francesco and Cremonesi, Stefano (2014) 'Partition functions of N=(2,2) gauge theories on S2 and vortices.', Communications in mathematical physics., 334 (3). pp. 1483-1527.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:16 December 2013
Date deposited:15 September 2017
Date of first online publication:17 July 2014
Date first made open access:15 September 2017

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