2d index and surface operators

By Abhijit Gadde, Sergei Gukov. 2013

253 citations recorded by the source corpus.

A bstractIn this paper we compute the superconformal index of 2d (2, 2) supersymmetric gauge theories. The 2d superconformal index, a.k.a. flavored elliptic genus, is computed by a unitary matrix integral much like the matrix integral that computes the 4d superconformal index. We compute the 2d index explicitly for a number of examples. In the case of abelian gauge theories we see that the index is invariant under flop transition and under CY-LG correspondence. The index also provides a powerful check of the Seiberg-type duality for non-abelian gauge theories discovered by Hori and Tong.In the later half of the paper, we study half-BPS surface operators in $ \mathcal{N} $ = 2 super-conformal gauge theories. They are engineered by coupling the 2d (2, 2) supersymmetric gauge theory living on the support of the surface operator to the 4d $ \mathcal{N} $ = 2 theory, so that different realizations of the same surface operator with a given Levi type are related by a 2d analogue of the Seiberg duality. The index of this coupled system is computed by using the tools developed in the first half of the paper. The superconformal index in the presence of surface defect is expected to be invariant under generalized S-duality. We demonstrate that it is indeed the case. In doing so the Seiberg-type duality of the 2d theory plays an important role.

Subfields: Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ba81c70de42b0b44d0cce28a546e308c1081d600

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Citations in the corpus

Comments on twisted indices in 3d supersymmetric gauge theories (2016, background): “The vortex loop defined as above is known to be invariant under the so-called hopping duality [5, 33] described in figure 3.”
A topologically twisted index for three-dimensional supersymmetric theories (2015, result): “Analogously, our results for four-dimensional theories are formally similar to those obtained for the elliptic genus in [4, 5, 23], and expressions for the one-loop determinants on S2 × T 2 have appeared in [24, 25].”
Defects and quantum Seiberg-Witten geometry (2014, background): “We refer the reader to [50, 58] for details of elliptic genera of the N = (0, 2) theories.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “These have appeared in the context of 4d partition functions in [21, 51, 52].”
M-Strings (2013, methodology): “The elliptic genus result for U(N) as computed in [7] reads as follows”
The geometry of supersymmetric partition functions (2013, background): “From the point of view of the (2, 0) theory on T (2), this partition function computes the elliptic genus, which is known to have modular properties under SL(2,Z) transformations of τ (see the recent papers [69-71] and references therein).”
General instanton counting and 5d SCFT (2014, background): “In fact, a similar problem was recently solved for the indices for the circle compactified 2d gauge theories [25–27].”