Branes and DAHA Representations
| Autor: | Gukov, Sergei, Koroteev, Peter, Nawata, Satoshi, Pei, Du, Saberi, Ingmar |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | SpringerBriefs in Mathematical Physics, volume 48, 2023 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/978-3-031-28154-9 |
| Popis: | 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. Comment: 95 pages, 22 figures, 2 tables |
| Databáze: | arXiv |
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