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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2411.14396 |
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| _version_ | 1866916491147870208 |
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| author | Moore, Gregory W. Saxena, Vivek Singh, Ranveer Kumar |
| author_facet | Moore, Gregory W. Saxena, Vivek Singh, Ranveer Kumar |
| contents | We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the diffeomorphism type of the spacetime and 't Hooft fluxes (characteristic classes of background gerbe connections, a.k.a. "one-form symmetry connections.") The example of $\mathcal{N}=2^*$ theories shows that, in general, the twisted partition functions depend on further topological data. We describe topological twisting for general four-dimensional $\mathcal{N}=2$ theories and argue that the topological partition functions depend on (a): the diffeomorphism type of the spacetime, (b): the characteristic classes of background gerbe connections and (c): a "generalized spin-c structure," a concept we introduce and define. The main ideas are illustrated with both Lagrangian theories and class $\mathcal{S}$ theories. In the case of class $\mathcal{S}$ theories of $A_1$ type, we note that the different $S$-duality orbits of a theory associated with a fixed UV curve $C_{g,n}$ can have different topological data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories Moore, Gregory W. Saxena, Vivek Singh, Ranveer Kumar High Energy Physics - Theory Mathematical Physics Algebraic Topology Differential Geometry Geometric Topology We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional $\mathcal{N}=2$ supersymmetric field theories. The original example of Donaldson-Witten theory depends only on the diffeomorphism type of the spacetime and 't Hooft fluxes (characteristic classes of background gerbe connections, a.k.a. "one-form symmetry connections.") The example of $\mathcal{N}=2^*$ theories shows that, in general, the twisted partition functions depend on further topological data. We describe topological twisting for general four-dimensional $\mathcal{N}=2$ theories and argue that the topological partition functions depend on (a): the diffeomorphism type of the spacetime, (b): the characteristic classes of background gerbe connections and (c): a "generalized spin-c structure," a concept we introduce and define. The main ideas are illustrated with both Lagrangian theories and class $\mathcal{S}$ theories. In the case of class $\mathcal{S}$ theories of $A_1$ type, we note that the different $S$-duality orbits of a theory associated with a fixed UV curve $C_{g,n}$ can have different topological data. |
| title | Topological Twisting of 4d $\mathcal{N}=2$ Supersymmetric Field Theories |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Topology Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2411.14396 |