Abstract
We introduce a first order description of linearized non-minimal (n = −1) supergravity in superspace, using the unconstrained prepotential superfield instead of the conventionally constrained super one forms. In this description, after integrating out the connection-like auxiliary superfield of first-order formalism, the superspace action is expressed in terms of a single superfield which combines the prepotential and compensator superfields. We use this description to construct the supersymmetric cubic interaction vertex 3/2 − 3/2 − 1/2 which describes the electromagnetic interaction between two non-minimal supergravity multiplets (superspin Y = 3/2 which contains a spin 2 and a spin 3/2 particles) and a vector multiplet (superspin Y = 1/2 contains a spin 1 and a spin 1/2 particles). Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength. This result generalize previous results for non-supersymmetric electromagnetic interactions of spin 2 particles. The constructed cubic interaction generates non-trivial deformations of the gauge transformations.
Highlights
The metric-like formulation, originates from early works [42,43,44,45,46,47,48,49], offers a more geometric viewpoint which together with the notion of higher spin connections [50] tries to extend our spin 2 intuition to higher spins
Exploring the trivial symmetries emerging between the two Y = 3/2 supermultiplets, we show that this cubic vertex must depend on the vector multiplet superfield strength
Cubic interactions Y1 − Y2 − Y3 among higher spin multiplets with superspins Y1, Y2, Y3 were first constructed in [69, 70] for the two cases of Y1 = s1 + 1/2, Y2 = Y3 and Y1 = s1, Y2 = Y3. These interactions are of the abelian type because the superspace cubic interaction Lagrangian is of the form L1 ∼ Φ1 W2 W3, where Φ1 is the set of superfields that describe the higher spin supermultiplet with superspin Y1 and W2, W3 are the gauge invariant superfield strengths for higher spin multiplets with superspins Y2, Y3 respectively
Summary
The power of first order formalism has been demonstrated repeatedly in the case of gravity, supergravity and higher spins. ∂(m1ξm2...ms) one can relax the symmetry for one of the indices and define a not fully s−1 symmetric tensor field enm1...ms−1 Checking the invariance of S[I] with respect to this local symmetry becomes more involved. This process is simplified by realizing that Iklm1...ms−1 satisfies the following identity. Which can be promoted to a Bianchi identity that enforces the a-transformation. This is s−1 achieved by introducing an auxiliary field, the connection, ωrnm1...ms−1 ) with a transformation law δωrnm1...ms−1 = ∂ranm1...ms−1. In this description the action takes symbolically the form. This action provides a first order formulation of the usual Fronsdal description [48, 49] and by integrating out the connection one recovers the action S[I]
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