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Exploring curved superspace (II)

  • Thomas T. Dumitrescu
  • Guido Festuccia
Article

Abstract

We extend our previous analysis of Riemannian four-manifolds \( \mathcal{M} \) admitting rigid supersymmetry to \( \mathcal{N} \) = 1 theories that do not possess a U(1) R symmetry. With one exception, we find that \( \mathcal{M} \) must be a Hermitian manifold. However, the presence of supersymmetry imposes additional restrictions. For instance, a supercharge that squares to zero exists, if the canonical bundle of the Hermitian manifold \( \mathcal{M} \) admits a nowhere vanishing, holomorphic section. This requirement can be slightly relaxed if \( \mathcal{M} \) is a torus bundle over a Riemann surface, in which case we obtain a supercharge that squares to a complex Killing vector. We also analyze the conditions for the presence of more than one supercharge. The exceptional case occurs when \( \mathcal{M} \) is a warped product S 3 × \( \mathbb{R} \), where the radius of the round S 3 is allowed to vary along \( \mathbb{R} \). Such manifolds admit two supercharges that generate the superalgebra OSp(1|2). If the S 3 smoothly shrinks to zero at two points, we obtain a squashed four-sphere, which is not a Hermitian manifold.

Keywords

Differential and Algebraic Geometry Superspaces Supergravity Models 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of PhysicsPrinceton UniversityPrincetonU.S.A
  2. 2.Institute for Advanced StudyPrincetonU.S.A.

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