2024/11/21 by Gregory W. Moore, Moore, Gregory W., Vivek Saxena +3
Physics and Astronomy · #Algebraic Topology (math.AT) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism
paper · pdf · doi:10.48550/arxiv.2411.14396
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We discuss what topological data must be provided to define topologically twisted partition functions of four-dimensional 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 N=2^* theories shows that, in general, the twisted partition functions depend on further topological data. We describe topological twisting for general four-dimensional 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 S theories. In the case of class S theories of A1 type, we note that the different S-duality orbits of a theory associated with a fixed UV curve Cg,n can have different topological data.