Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 5, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP05(2013)017
Keywords
Supersymmetric gauge theory; Field Theories in Lower Dimensions; Differential and Algebraic Geometry; Supergravity Models
Categories
Funding
- DOE
- Princeton University
- NSF [PHY-0969448]
- Institute for Advanced Study
- Peter and Patricia Gruber Awards
- Robert Rees Fund for Applied Research
- Israel Science Foundation [884/11]
- United States-Israel Binational Science Foundation (BSF) [2010/629]
- DOE
- Princeton University
- NSF [PHY-0969448]
- Institute for Advanced Study
- Peter and Patricia Gruber Awards
- Robert Rees Fund for Applied Research
- Israel Science Foundation [884/11]
- United States-Israel Binational Science Foundation (BSF) [2010/629]
- Direct For Mathematical & Physical Scien [969448] Funding Source: National Science Foundation
- Division Of Physics [969448] Funding Source: National Science Foundation
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We construct supersymmetric field theories on Riemannian three-manifolds M, focusing on N = 2 theories with a U(1) R symmetry. Our approach is based on the rigid limit of new minimal supergravity in three dimensions, which couples to the flat-space supermultiplet containing the R-current and the energy-momentum tensor. The field theory on M possesses a single supercharge if and only if M admits an almost contact metric structure that satisfies a certain integrability condition. This may lead to global restrictions on M, even though we can always construct one supercharge on any given patch. We also analyze the conditions for the presence of additional supercharges. In particular, two supercharges of opposite R-charge exist on every Seifert manifold. We present general supersymmetric Lagrangians on M and discuss their flat-space limit, which can be analyzed using the R-current supermultiplet. As an application, we show how the flat-space two-point function of the energy-momentum tensor in N = 2 superconformal theories can be calculated using localization on a squashed sphere.
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