Branes and DAHA Representations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866910781349560320 |
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| author | Gukov, Sergei Koroteev, Peter Nawata, Satoshi Pei, Du Saberi, Ingmar |
| author_facet | Gukov, Sergei Koroteev, Peter Nawata, Satoshi Pei, Du Saberi, Ingmar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_03565 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Branes and DAHA Representations Gukov, Sergei Koroteev, Peter Nawata, Satoshi Pei, Du Saberi, Ingmar High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Algebra Representation Theory 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. |
| title | Branes and DAHA Representations |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2206.03565 |