Twisted traces on abelian quantum Higgs and Coulomb branches
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866915411476348928 |
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| author | Gaiotto, Davide Hilburn, Justin Redondo-Yuste, Jaime Webster, Ben Zhou, Zheng |
| author_facet | Gaiotto, Davide Hilburn, Justin Redondo-Yuste, Jaime Webster, Ben Zhou, Zheng |
| contents | We study twisted traces on the quantum Higgs branches $A_{\operatorname{Higgs}}$ of $3d, \mathcal{N}=4$ gauge theories, that is, the quantum Hamiltonian reductions of Weyl algebras. In theories which are good, we define a twisted trace that arises naturally from the correlation functions of the gauge theory. We show that this trace induces an inner product and a short star product on $A_{\operatorname{Higgs}}$.
We analyze this trace in the case of an abelian gauge group and show that it has a natural expansion in terms of the twisted traces of Verma modules, confirming a conjecture of the first author and Okazaki. This expansion has a natural interpretation in terms of 3-d mirror symmetry, and we predict that it can be interpreted as an Atiyah-Bott fixed-point formula under the quantum Hikita isomorphism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15198 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Twisted traces on abelian quantum Higgs and Coulomb branches Gaiotto, Davide Hilburn, Justin Redondo-Yuste, Jaime Webster, Ben Zhou, Zheng High Energy Physics - Theory Mathematical Physics Rings and Algebras We study twisted traces on the quantum Higgs branches $A_{\operatorname{Higgs}}$ of $3d, \mathcal{N}=4$ gauge theories, that is, the quantum Hamiltonian reductions of Weyl algebras. In theories which are good, we define a twisted trace that arises naturally from the correlation functions of the gauge theory. We show that this trace induces an inner product and a short star product on $A_{\operatorname{Higgs}}$. We analyze this trace in the case of an abelian gauge group and show that it has a natural expansion in terms of the twisted traces of Verma modules, confirming a conjecture of the first author and Okazaki. This expansion has a natural interpretation in terms of 3-d mirror symmetry, and we predict that it can be interpreted as an Atiyah-Bott fixed-point formula under the quantum Hikita isomorphism. |
| title | Twisted traces on abelian quantum Higgs and Coulomb branches |
| topic | High Energy Physics - Theory Mathematical Physics Rings and Algebras |
| url | https://arxiv.org/abs/2308.15198 |