Effective action in general chiral superfield model

According to the superstring theory the low-energy elementary particle models contain as ingredient the multiplets of chiral and antichiral superfields action of which is given in terms of kählerian effective potential K(¯ Φ, Φ) and chiral W (Φ) and antichiral ¯ W (¯ Φ) potentials. These potentials are found in explicit and closed form within string perturbation theory (see f.e. [1]). Phe-nomenological aspects of such models have been studied in recent papers [2]. In quantum theory one can expect an appearance of quantum corrections to the potentials K(¯ Φ, Φ) and W (Φ). As a result we face a problem of calculating effective action in models with arbitrary functions K(¯ Φ, Φ) and W (Φ). The remarkable features of the massless theories with N = 1 chiral su-perfields are the possibilities of obtaining the chiral quantum corrections. A few years ago West [3] pointed out that finite two-loop chiral contribution to effective action really arises in massless Wess-Zumino model (see also [4]). In this talk we consider the general problem of calculating leading quantum correction to chiral potential and kählerian potential in theory with arbitrary potentials K(¯ Φ, Φ) and W (Φ), ¯ W (¯ Φ). The remarkable result we obtain here is that despite the theory under consideration is non-renormalizable at arbitrary K(¯ Φ, Φ), W (Φ), the lower (two-loop) chiral correction to effective action is always finite. We consider N = 1 supersymmetric field theory with action S[ ¯ Φ, Φ] = d 8 zK(¯ Φ, Φ) + (d 6 zW (Φ) + h.c.) (1) where Φ(z) and ¯ Φ(z) are chiral and antichiral superfields respectively. As well known, the real function K(¯ Φ, Φ) is called kählerian potential and holomorphic function W (Φ) is called chiral potential [5]. The partial cases of the theory (1) are Wess-Zumino model with K(¯ Φ, Φ) = Φ ¯ Φ, W (Φ) ∼ Φ 3 and N = 1 supersymmetric four-dimensional sigma-model with W (Φ) = 0. The action (1) is a most general one constructed from chiral and antichiral superfields which does not contain the higher derivatives at component level. Therefore it is natural to call the theory (1) a general chiral superfield model. Let Γ[ ¯ Φ, Φ] be effective action in the model (1). Within a momentum expansion the effective action can be presented as a series in supercovariant 1