English

S-duality and the N=2 Lens Space Index

High Energy Physics - Theory 2013-11-06 v2

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.

Keywords

Cite

@article{arxiv.1306.1543,
  title  = {S-duality and the N=2 Lens Space Index},
  author = {Shlomo S. Razamat and Masahito Yamazaki},
  journal= {arXiv preprint arXiv:1306.1543},
  year   = {2013}
}

Comments

33 pages, 3 figures, harvmac. v2: minor corrections