On the construction of linearized N = 1 supergravities coupled to matter

Abstract

We present a modified formulation of minimal N = 1 linearized supergravity coupled to generic N = 1 supersymmetric matter. The formalism is based on the superprojectors, superspin-transition operators, vector and scalar superfield. Such approach has some advantages for finding superpropagators.In general, the theory of N = 1 supergravity is well known (see for review of standard supergravity [1]), but here we present quite interesting approach of a version of minimal N = 1 supergravity coupled to generic N = 1 supersymmetric matter. The formalism is based on the superprojectors, vector and scalar superfield, such approach has explicit supersymmetric invariance and some advantages for finding superpropagators. Also, using the superspin-transition operators we can construct operators that give gauge transformations and source constraints. This means that the gauge transformations and source constraints are not proposed, but follow directly from given equation.We start from a massive superfield equation and find the corresponding massless equation, which allows us to introduce certain gauge transformations and source constraints. Some general considerations from equation of motions for ordinary fields are transferred to the superfield case in [2]. Here we use the modified formalism of superspin projection operators, previously exploited in our papers [3,4], which turns out to be quite fruitful both in the ordinary field and in the superfield cases. In the N = 1 case projectors method was developed by Sokatchev [5], in [6] the projectors method was generalized to the arbitrary N case. We use the modified version of superprojectors given in [7]. In our case we first proceed from a given equation and then obtain the consistent bilinear form and the Lagrangian. Therefore our equations admit a derivation from a superfield Lagrangian. The alternative Lagrangian approach to superfields has been recently treated in [8,9].A superfield is a function of space-time coordinates x and anticommuting Grassmann variables θ. θ is four-component Majorana spinor. The general superfield φ i (x, θ) transforming according to the irreducible Lorentz representation i may be * ) Presented at