Symmetries of supergravity backgrounds and supersymmetric field theory

Abstract

Abstract In four spacetime dimensions, all N $$ \mathcal{N} $$ = 1 supergravity-matter systems can be formulated in the so-called U(1) superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background U(1) superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields ℓ α 1 … α m α ⋅ 1 … α ⋅ n $$ {\mathrm{\ell}}_{\left({\alpha}_1\dots {\alpha}_m\right)\left({\overset{\cdot }{\alpha}}_1\dots {\overset{\cdot }{\alpha}}_n\right)} $$ , 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 ℓ α α ⋅ $$ {\mathrm{\ell}}_{\alpha \overset{\cdot }{\alpha }} $$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields ℓ α 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.

Keywords

• Supergravity Models
• Superspaces