Exploring curved superspace

By T. Dumitrescu, G. Festuccia, N. Seiberg. 2012

281 citations recorded by the source corpus.

A bstractWe systematically analyze Riemannian manifolds $ \mathcal{M} $ that admit rigid supersymmetry, focusing on four-dimensional $ \mathcal{N} = {1} $ theories with a U(1)R symmetry. We find that $ \mathcal{M} $ admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on $ \mathcal{M} $. We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that $ \mathcal{M} $ is locally isometric to $ {\mathcal{M}_3} \times \mathbb{R} $, where $ {\mathcal{M}_3} $ is a maximally symmetric space.

Subfields: Applied Mathematics, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/fec69249904bd5240f96d6d462ebd53492124d09

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In Applied Mathematics

In Mathematical Physics

In Nuclear and High Energy Physics

Citations in the corpus

Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes (2018, result): “ent language is [46] D "+ iVnm 5 " i 2 (Vnm) 5 "= 0: (4.5) 6The new minimal supergravity elds Anm, Vnm are not uniquely dened by the conformal supergravity eld Acs. As shown in [48], they can be shifted by a term proportional to K dx, where K@ is the supersymmetric Killing vector o”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, methodology): “Four-dimensional N = 1 supersymmetric backgrounds coupling to theR-multiplet12 are only possible forM4 a complex manifold [6, 7].”
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].”
Bootstrapping the superconformal index with surface defects (2012, background): “d supersymmetric quantum eld theories by placing them on curved compact manifolds, notably (squashed) spheres.1 In several cases 1More general susy-preserving backgrounds are beginning to be explored [1, 2]. { 1 { localization techniques have facilitated the exact calculation of the partition functi”
The Casimir energy in curved space and its supersymmetric counterpart (2015, background): “Its evaluation on the S3 × S1 background [17] yields29”
The geometry of supersymmetric partition functions (2013, methodology): “In the compact case, they include the flat torus T 4 and S3 × S1 with the usual round metric [1, 9].”
Supersymmetric field theories on three-manifolds (2012, methodology): “(See [27] for a related discussion in four dimensions.”
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.”
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.”