Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 10, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP10(2014)062
Keywords
Supersymmetric gauge theory; Wilson; 't Hooft and Polyakov loops; Nonperturbative Effects; Topological Field Theories
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Funding
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
- ERC STG grant [306260]
- Royal Society Dorothy Hodgkin fellowship
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Research and Innovation
- ERC STG grant [306260]
- Royal Society Dorothy Hodgkin fellowship
- EPSRC [EP/J019518/1] Funding Source: UKRI
- STFC [ST/G000522/1, ST/J000329/1, ST/L000458/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/J019518/1] Funding Source: researchfish
- Science and Technology Facilities Council [ST/G000522/1, ST/L000458/1, ST/J000329/1] Funding Source: researchfish
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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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