Abstract
In this paper we continue the study of the superconformal index of fourdimensional 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 RuijsenaarsSchneider system. The structure constants of the algebra are elliptic generalizations of the LittlewoodRichardson coefficients. In the Macdonald limit, we identify the difference operators with local operators in the twodimensional TQFT interpretation of the superconformal index. We also study the dimensional reduction to difference operators acting on the threesphere 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 fourdimensional N =2* theory on a foursphere by embedding the threedimensional theory as an Sduality domain wall.
Original language  English 

Article number  62 
Journal  Journal of High Energy Physics 
Volume  2014 
Issue number  62 
DOIs  
Publication status  Published  Oct 2014 
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Lotte Hollands
 School of Mathematical & Computer Sciences  Associate Professor
 School of Mathematical & Computer Sciences, Mathematics  Associate Professor
Person: Academic (Research & Teaching)