Supersymmetric field theories on three-manifolds

By Cyril Closset, T. Dumitrescu, G. Festuccia, Z. Komargodski. 2012

296 citations recorded by the source corpus.

A bstractWe construct supersymmetric field theories on Riemannian three-manifolds $ \mathcal{M} $, focusing on $ \mathcal{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 $ \mathcal{M} $ possesses a single supercharge if and only if $ \mathcal{M} $ admits an almost contact metric structure that satisfies a certain integrability condition. This may lead to global restrictions on $ \mathcal{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 $ \mathcal{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 $ \mathcal{N} $ = 2 superconformal theories can be calculated using localization on a squashed sphere.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/b0d7800a39f4ed5d8e1e1a257aa2d8f2ebb2745f

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

The geometry of supersymmetric partition functions (2013, methodology): “The corresponding supergravity theory was recently studied in superspace [19–21], as well as in components [3, 4, 16].”
Supersymmetry on curved spaces and holography (2012, methodology): “3) This problem has been studied very detailed also in [58].”
Exact results for the entanglement entropy and the energy radiated by a quark (2013, background): “They applied the results of [42] to look for supersymmetric regularized spheres.”
Bootstrapping SCFTs with four supercharges (2015, unknown): “In [54], it was shown how τRR can be computed for d = 3, N = 2 SCFTs from the squashed-sphere partition function F (b)”
A topologically twisted index for three-dimensional supersymmetric theories (2015, background): “More general supersymmetric backgrounds have been constructed in [48, 49], and the dependence of the partition function on the background has been studied in [50].”
Comments on twisted indices in 3d supersymmetric gauge theories (2016, methodology): “42) are mixed CS terms between abelian vector multiplets and the R-symmetry gauge field in the new-minimal supergravity multiplet [42, 44], which is given by”
Localization techniques in quantum field theories (2016, methodology): “2In this article, our notations and spinor conventions will mostly follow [4].”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “This leads to the conventions of [27] when reducing to 3d along the second 4d coordinate, x(2) = y, like in appendix D of [8].”
Localization on Hopf surfaces (2014, methodology): “8) is precisely of the form implied by new minimal supersymmetry in three dimensions [27], and used in the analysis of [10].”