Supersymmetry on curved spaces and holography

By Claudius Klare, A. Tomasiello, Alberto Zaffaroni. 2012

205 citations recorded by the source corpus.

A bstractWe study superconformal and supersymmetric theories on Euclidean four- and three-manifolds with a view toward holographic applications. Preserved supersymmetry for asymptotically locally AdS solutions implies the existence of a (charged) “conformal Killing spinor” on the boundary. We study the geometry behind the existence of such spinors. We show in particular that, in dimension four, they exist on any complex manifold. This implies that a superconformal theory has at least one supercharge on any such space, if we allow for a background field (in general complex) for the R-symmetry. We also show that this is actually true for any supersymmetric theory with an R-symmetry. We also analyze the three-dimensional case and provide examples of supersymmetric theories on Sasaki spaces.

Subfields: Astronomy and Astrophysics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/9ba20a19ed1b6cf0a2d91d064304000d69e09578

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Citations in the corpus

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, unknown): “[44, 45]).”
Localization on Hopf surfaces (2014, background): “As already noted, a priori in Euclidean signature the fermionic fields λ, λ̃ are independent, and the bosonic fields Aµ, D are not Hermitian.”
Supersymmetric field theories on three-manifolds (2012, methodology): “A similar analysis in [26] found the integrability condition εPμ∂νPρ = 0, which is locally equivalent to (4.”
The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere (2012, background): “For a recent discussion on related issues in three and four dimensions one may consult [29, 30, 31].”
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].”
Seiberg-Witten theories on ellipsoids (2012, methodology): “Some systematic analysis has been made in [12, 13, 14, 15, 16] to draw conditions on the background geometry from Killing spinor equation.”
Exploring curved superspace (2012, background): “It was recently studied in the context of conformal supergravity [6].”
The geometry of supersymmetric partition functions (2013, background): “These equations were analyzed in [16] (see also [14, 22]).”
The Casimir energy in curved space and its supersymmetric counterpart (2015, background): “We recall that two such Killing vectors exist in Euclidean backgrounds preserving two supercharges of opposite R-charge [16, 17].”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “Four-dimensional N = 1 supersymmetric backgrounds coupling to theR-multiplet12 are only possible forM4 a complex manifold [6, 7].”