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arXiv · 1209.5408

Exploring Curved Superspace (II)

Thomas T. Dumitrescu·Guido Festuccia
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Abstract

We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N=1 theories that do not possess a U(1)_R symmetry. With one exception, we find that 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 M admits a nowhere vanishing, holomorphic section. This requirement can be slightly relaxed if 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 M is a warped product S^3 x R, where the radius of the round S^3 is allowed to vary along 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.

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Thomas T. Dumitrescu, Guido Festuccia. 2012-10-18. Exploring Curved Superspace (II). https://doi.org/10.1007/jhep01(2013)072

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