Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 12, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP12(2021)181
Keywords
Supersymmetric Gauge Theory; Topological Field Theories
Categories
Funding
- Infosys Endowment for the study of the Quantum Structure of Spacetime
- SERB Ramanujan fellowship
- National Science Foundation [PHY-1607611]
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The study discusses the modular property of supersymmetric partition functions in four dimensions and explores the consistency of gluing operations on different topological spaces. The research results play a crucial role in physical calculations such as computing the entropy of supersymmetric black holes.
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric partition function of two-dimensional supersymmetric theories on a torus i.e. of the elliptic genus. The partition functions in question are on manifolds homeomorphic to the ones obtained by gluing solid tori. Such gluing involves the choice of a large diffeomorphism of the boundary torus, along with the choice of a large gauge transformation for the background flavor symmetry connections, if present. Our modular property is a manifestation of the consistency of the gluing procedure. The modular property is used to rederive a supersymmetric Cardy formula for four dimensional gauge theories that has played a key role in computing the entropy of supersymmetric black holes. To be concrete, we work with four-dimensional N = 1 supersymmetric theories but we expect versions of our result to apply more widely to supersymmetric theories in other dimensions.
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