期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 1, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP01(2014)124
关键词
Supersymmetric gauge theory; Extended Supersymmetry; Differential and Algebraic Geometry; Supergravity Models
资金
- Fundamental Laws Initiative of the Center for the Fundamental Laws of Nature at Harvard University
- DOE [DE-SC0007870]
- NSF [PHY-0847457, PHY-1067976, PHY-0756966, PHY-0969448]
- Centennial Fellowship from Princeton University
- Peter and Patricia Gruber Awards
- Rosa and Emilio Segre research award
- Robert Rees Fund for Applied Research
- Israel Science Foundation [884/11, 1937/12]
- United States-Israel Binational Science Foundation (BSF) [2010/629]
- I-CORE Program of the Planning and Budgeting Committee
- Fundamental Laws Initiative of the Center for the Fundamental Laws of Nature at Harvard University
- DOE [DE-SC0007870]
- NSF [PHY-0847457, PHY-1067976, PHY-0756966, PHY-0969448]
- Centennial Fellowship from Princeton University
- Peter and Patricia Gruber Awards
- Rosa and Emilio Segre research award
- Robert Rees Fund for Applied Research
- Israel Science Foundation [884/11, 1937/12]
- United States-Israel Binational Science Foundation (BSF) [2010/629]
- I-CORE Program of the Planning and Budgeting Committee
We consider supersymmetric field theories on compact manifolds M and obtain constraints on the parameter dependence of their partition functions Z(M). Our primary focus is the dependence of Z(M) on the geometry of M, as well as background gauge fields that couple to continuous flavor symmetries. For N = 1 theories with a U(1) R symmetry in four dimensions, M must be a complex manifold with a Hermitian metric. We find that Z(M) is independent of the metric and depends holomorphically on the complex structure moduli. Background gauge fields define holomorphic vector bundles over M and Z(M) is a holomorphic function of the corresponding bundle moduli. We also carry out a parallel analysis for three-dimensional N = 2 theories with a U(1) R symmetry, where the necessary geometric structure on M is a transversely holomorphic foliation (THF) with a transversely Hermitian metric. Again, we find that ZM is independent of the metric and depends holomorphically on the moduli of the THF. We discuss several applications, including manifolds diffeomorphic to S-3 x S-1 or S-2 x S-1, which are related to supersymmetric indices, and manifolds diffeomorphic to S-3 (squashed spheres). In examples where Z(M) has been calculated explicitly, our results explain many of its observed properties.
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