Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices

By F. Benini, Stefano Cremonesi. 2012

304 citations recorded by the source corpus.

We apply localization techniques to compute the partition function of a two-dimensional $${\mathcal{N}=(2,2)}$$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.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/077406154cd985ae479a38a543b5ddd7be20eae5

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In Nuclear and High Energy Physics

Citations in the corpus

Two-Sphere Partition Functions and Gromov–Witten Invariants (2012, methodology): “The partition function for such a GLSM on S2, deformed appropriately by O( 1 R ) terms and localized onto the Coulomb branch, takes the form [22,23]8”
Correlation functions of Coulomb branch operators (2016, background): “irection here and concentrate on N= 2 theories in d= 4. In fact, technically the case of d = 2 is simpler since no new instanton contributions need to be computed in the Coulomb branch representation [1,2]. 2 the operator mixing matrix on S4 a la Gram-Schmidt leads to a representation of the extrema”