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arXiv · 1306.1543

S-duality and the N=2 Lens Space Index

Shlomo S. Razamat·Masahito Yamazaki
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Abstract

We discuss some of the analytic properties of lens space indices for 4d N=2 theories of class S. The S-duality properties of these theories highly constrain the lens space indices, and imply in particular that they are naturally acted upon by a set of commuting difference operators corresponding to surface defects. We explicitly identify the difference operators to be a matrix-valued generalization of the elliptic Ruijsenaars-Schneider model. In a special limit these difference operators can be expressed naturally in terms of Cherednik operators appearing in the double affine Hecke algebras, with the eigenfunctions given by non-symmetric Macdonald polynomials.

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Shlomo S. Razamat, Masahito Yamazaki. 2013-10-02. S-duality and the N=2 Lens Space Index. https://doi.org/10.1007/jhep10(2013)048

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