Schur Quantization and Complex Chern-Simons theory
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917694862786560 |
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| author | Gaiotto, Davide Teschner, Jörg |
| author_facet | Gaiotto, Davide Teschner, Jörg |
| contents | Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a certain complex symplectic manifold called the "K-theoretic Coulomb branch" of the theory. The collection of K-theoretic Coulomb branches include many complex phase spaces of great interest, including in particular the "character varieties" of complex flat connections on a Riemann surface. The SQFT definition endows K-theoretic Coulomb branches with a variety of canonical structures, including a deformation quantization. In this paper we introduce a canonical "Schur" quantization of K-theoretic Coulomb branches. It is defined by a variant of the Gelfand-Naimark-Segal construction, applied to protected Schur correlation functions of half-BPS line defects. Schur quantization produces an actual quantization of the complex phase space. As a concrete application, we apply this construction to character varieties in order to quantize Chern-Simons gauge theory with a complex gauge group. Other applications include the definition of a new quantum deformation of the Lorentz group, and the solution of certain spectral problems via dualities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09171 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Schur Quantization and Complex Chern-Simons theory Gaiotto, Davide Teschner, Jörg High Energy Physics - Theory Quantum Algebra Any four-dimensional Supersymmetric Quantum Field Theory with eight supercharges can be associated to a certain complex symplectic manifold called the "K-theoretic Coulomb branch" of the theory. The collection of K-theoretic Coulomb branches include many complex phase spaces of great interest, including in particular the "character varieties" of complex flat connections on a Riemann surface. The SQFT definition endows K-theoretic Coulomb branches with a variety of canonical structures, including a deformation quantization. In this paper we introduce a canonical "Schur" quantization of K-theoretic Coulomb branches. It is defined by a variant of the Gelfand-Naimark-Segal construction, applied to protected Schur correlation functions of half-BPS line defects. Schur quantization produces an actual quantization of the complex phase space. As a concrete application, we apply this construction to character varieties in order to quantize Chern-Simons gauge theory with a complex gauge group. Other applications include the definition of a new quantum deformation of the Lorentz group, and the solution of certain spectral problems via dualities. |
| title | Schur Quantization and Complex Chern-Simons theory |
| topic | High Energy Physics - Theory Quantum Algebra |
| url | https://arxiv.org/abs/2406.09171 |