Higher derivative invariants in four dimensional 𝒩 = 3 Poincaré supergravity

Abstract

In this paper we use the superconformal approach to derive the higher derivative action for 𝒩 = 3 Poincaré supergravity in four space-time dimensions. We first study the coupling of 𝒩 = 3 vector multiplets to conformal supergravity. Thereafter we combine it with the pure 𝒩 = 3 conformal supergravity action and use a minimum of three vector multiplets as compensators to arrive at Poincaré supergravity with higher derivative corrections. We give a general prescription on how to eliminate the auxiliary fields in an iterative manner and obtain the supergravity action order by order in derivatives. We also show that the truncation of the action at fourth order in derivatives is a consistent truncation.