ar X iv : h ep - t h / 96 04 15 4 v 1 2 5 A pr 1 99 6 On quantum model of supergravity compensator

A new N = 1 superfield model in D = 4 flat superspace is suggested. This model describes dynamics of chiral compensator and can be treated as a low-energy limit of D = 4, N = 1 quantum superfield supergravity. Renormalization structure of this model is studied and one-loop counterterms are calculated. It is shown that the theory is infrared free. An effective action for the model under consideration is investigated in infrared domain. The lower contributions to the one-loop effective action are computed in explicit form. 1. It is well known that four-dimensional simple supergravity can be formulated in N = 1 curved superspace in terms of vector superfield H m (z) and chiral Φ(z) and antichiral ¯ Φ(z) compensators [1-3] (see also [4]). Here as usual z m ≡ (x m , θ µ , ¯ θ ˙ µ) are the superspace coordinates. General approach to quantum superfield supergravity has been developed in refs. [5,6]. However a number of concrete quantum aspects has not been investigated in details because of complicated enough structure of the superfield supergravity itself. Our goal in the present paper is to formulate a simplified model associated with N = 1, D = 4 superfield supergravity and describing a dynamics only of compensator superfields in flat superspace. We show that this model makes possible to carry out a detailed investigation of many quantum aspects and possessses remarkable properties in infrared domain. It allows to treat such a model as a natural low-energy limit of quantum superfield supergravity with matter. The model under consideration is based on an idea of induced gravity. An approach to four-dimensional quantum gravity model induced by conformal anomaly of matter fields in curved space-time has been suggested in ref. [6]. It has been shown that this model is super-renormalizable in infrared limit and infrared free. In the given paper we present a supersymmetric model of induced quantum gravity and investigate its quantum aspects. 2. We start with known superconformal anomaly in N = 1 curved superspace. This anomaly is formulated in terms of supercurrent and supertrace [7,8] (see also [4]) which are the superfield analogs of the energy-momentum tensor and its trace respectively. For superconformally invariant theories the classical supertrace V vanishes. However in quantum theory the supertrace V is not equal to zero because of superconformal anomaly and can be written as follows [9,10,4]