Chiral supergravity actions and superforms

Abstract

The superform construction of supergravity actions, christened the "ectoplasm method," is based on the use of a closed super d-form in the case of d space-time dimensions. In known examples, such superforms are obtained by iteratively solving nontrivial cohomological problems. The latter usually makes this scheme no less laborious than the normal coordinate method for deriving component actions for matter-coupled supergravity. In this note we present an alternative procedure to generate required superforms in four space-time dimensions, which makes use of self-dual vector multiplets. It provides the shortest derivation of chiral actions in two different theories: (i) N = 1 old minimal supergravity; and (ii) N = 2 conformal supergravity. The N = 2 superform construction is developed here for the first time. Although our consideration is restricted to the case of four dimensions, a generalization to higher dimensions is plausible.

14 pages; V2: minor corrections

References in corpus (6)

• 4D N = 2 Supergravity and Projective Superspace
• On conformal supergravity and projective superspace
• The ultra-violet question in maximally supersymmetric field theories
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• On N = 2 supergravity and projective superspace: Dual formulations
• Ectoplasm & Superspace Integration Measure for 2D Supergravity with Four Spinorial Supercurrents

Cited by in corpus (9)

• N=2 Conformal Superspace in Four Dimensions
• Invariants for minimal conformal supergravity in six dimensions
• New higher-derivative couplings in 4D N = 2 supergravity
• Component reduction in N=2 supergravity: the vector, tensor, and vector-tensor multiplets
• Rigid 4D N=2 supersymmetric backgrounds and actions
• The linear multiplet and ectoplasm
• On 2D N=(4,4) superspace supergravity
• Superforms in Simple Six-dimensional Superspace
• Superspace de Rham Complex and Relative Cohomology