B-twisted Gaiotto-Witten theory and topological quantum field theory
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| Format: | Preprint |
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2024
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| _version_ | 1866914657341538304 |
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| author | Garner, Niklas Geer, Nathan Young, Matthew B. |
| author_facet | Garner, Niklas Geer, Nathan Young, Matthew B. |
| contents | We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto-Witten theory with linear matter. Our constructions are based on relative modular structures on the category of weight modules over an unrolled quantization of a Lie superalgebra. The Lie superalgebra, originally defined by Gaiotto and Witten, is associated to a complex symplectic representation of a metric abelian Lie algebra. The physical theories we model admit alternative realizations as Chern-Simons-Rozansky-Witten theories and supergroup Chern-Simons theories and include as particular examples global forms of $\mathfrak{gl}(1 \vert 1)$-Chern-Simons theory and toral Chern-Simons theory. Fundamental to our approach is the systematic incorporation of non-genuine line operators which source flat connections for the topological flavour symmetry of the theory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_16192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | B-twisted Gaiotto-Witten theory and topological quantum field theory Garner, Niklas Geer, Nathan Young, Matthew B. Representation Theory High Energy Physics - Theory Quantum Algebra Primary 57R56, Secondary 17B10 We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto-Witten theory with linear matter. Our constructions are based on relative modular structures on the category of weight modules over an unrolled quantization of a Lie superalgebra. The Lie superalgebra, originally defined by Gaiotto and Witten, is associated to a complex symplectic representation of a metric abelian Lie algebra. The physical theories we model admit alternative realizations as Chern-Simons-Rozansky-Witten theories and supergroup Chern-Simons theories and include as particular examples global forms of $\mathfrak{gl}(1 \vert 1)$-Chern-Simons theory and toral Chern-Simons theory. Fundamental to our approach is the systematic incorporation of non-genuine line operators which source flat connections for the topological flavour symmetry of the theory. |
| title | B-twisted Gaiotto-Witten theory and topological quantum field theory |
| topic | Representation Theory High Energy Physics - Theory Quantum Algebra Primary 57R56, Secondary 17B10 |
| url | https://arxiv.org/abs/2401.16192 |