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The superconformal index and an elliptic algebra of surface defects.

Bullimore, Mathew and Fluder, Martin and Hollands, Lotte and Richmond, Paul (2014) 'The superconformal index and an elliptic algebra of surface defects.', Journal of high energy physics., 2014 (10). 062.


In this paper we continue the study of the superconformal index of four-dimensional N =2 theories of class S in the presence of surface defects. Our main result is the construction of an algebra of difference operators, whose elements are labeled by irreducible representations of A N −1. For the fully antisymmetric tensor representations these difference operators are the Hamiltonians of the elliptic Ruijsenaars-Schneider system. The structure constants of the algebra are elliptic generalizations of the Littlewood-Richardson coefficients. In the Macdonald limit, we identify the difference operators with local operators in the two-dimensional TQFT interpretation of the superconformal index. We also study the dimensional reduction to difference operators acting on the three-sphere partition function, where they characterize supersymmetric defects supported on a circle, and show that they are transformed to supersymmetric Wilson loops under mirror symmetry. Finally, we compare to the difference operators that create ’t Hooft loops in the four-dimensional N =2* theory on a four-sphere by embedding the three-dimensional theory as an S-duality domain wall.

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Publisher statement:© The Author(s) 2014 Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Date accepted:25 September 2014
Date deposited:08 June 2018
Date of first online publication:09 October 2014
Date first made open access:No date available

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