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arXiv · 2206.03565

Branes and DAHA Representations

Sergei Gukov·Peter Koroteev·Satoshi Nawata·Du Pei·Ingmar Saberi
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Abstract

Using brane quantization, we study the representation theory of the spherical double affine Hecke algebra of type $A_1$ in terms of the topological A-model on the moduli space of flat SL(2,C)-connections on a once-punctured torus. In particular, we provide an explicit match between finite-dimensional representations and A-branes with compact support; one consequence is the discovery of new finite-dimensional indecomposable representations. We proceed to embed the A-model story in an M-theory brane construction, closely related to the one used in the 3d/3d correspondence; as a result, we identify modular tensor categories behind particular finite-dimensional representations with PSL(2,Z) action. Using a further connection to the fivebrane system for the class S construction, we go on to study the relationship of Coulomb branch geometry and algebras of line operators in 4d N=2* theories to the double affine Hecke algebra.

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Sergei Gukov, Peter Koroteev, Satoshi Nawata, Du Pei, Ingmar Saberi. 2022-06-07. Branes and DAHA Representations. https://doi.org/10.1007/978-3-031-28154-9

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