Symmetries of supergravity backgrounds and supersymmetric field theory

Abstract

In four spacetime dimensions, all $\mathcal{N}=1$ supergravity-matter systems can be formulated in the so-called $\mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background $\mathsf{U}(1)$ superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields ${\ell }_{({\alpha }_1\dots {\alpha }_m)({\dot{\alpha }}_1\dots {\dot{\alpha }}_n)}$, with $m$ and $n$ non-negative integers, $m+n>0$, and elaborate on their significance in the following cases: (i) $m=n=1$; (ii) $m-1=n=0$; and (iii) $m=n>1$. The (conformal) Killing vector superfields ${\ell }_{\alpha \dot{\alpha }}$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields ${\ell }_{\alpha }$ generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with $m=n>1$ prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.

arXiv comment58 pages; V2: typos corrected, references added

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Cited by in corpus (17)

• Duality-invariant (super)conformal higher-spin models
• Extended superconformal higher-spin gauge theories in four dimensions
• Superconformal geometries and local twistors
• Conformal interactions between matter and higher-spin (super)fields
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