期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 8, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP08(2017)090
关键词
Supersymmetric Gauge Theory; Supersymmetry and Duality; Anomalies in Field and String Theories; Duality in Gauge Field Theories
资金
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development Innovation
- John Templeton Foundation
- National Science Foundation [NSF PHY11-25915]
- Perimeter Institute for Theoretical Physics
- Government of Canada through Industry Canada
- Province of Ontario through the Ministry of Economic Development Innovation
- John Templeton Foundation
- National Science Foundation [NSF PHY11-25915]
We compute the supersymmetric partition function of N = 1 supersymmetric gauge theories with an R-symmetry on M-4 congruent to M-g,M-p x S-1, a principal elliptic fiber bundle of degree p over a genus-g Riemann surface, Sigma(g). Equivalently, we compute the generalized supersymmetric index I-Mg,(p), with the supersymmetric three-manifold M-g,M-p as the spatial slice. The ordinary N = 1 supersymmetric index on the round three-sphere is recovered as a special case. We approach this computation from the point of view of a topological A-model for the abelianized gauge fields on the base Sigma(g). This A-model - or A-twisted two-dimensional N = (2; 2) gauge theory encodes all the information about the generalized indices, which are viewed as expectations values of some canonically-defined surface defects wrapped on T-2 inside Sigma(g) x T-2. Being de fined by compactification on the torus, the A model also enjoys natural modular properties, governed by the four-dimensional 't Hooft anomalies. As an application of our results, we provide new tests of Seiberg duality. We also present a new evaluation formula for the three-sphere index as a sum over two-dimensional vacua.
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