Holomorphic effective potential in general chiral superfield model

TL;DR

This paper calculates the two-loop holomorphic effective potential in a general chiral superfield model, relevant for low-energy superstring theory, providing a finite correction formula involving derivatives of the superpotential and Kähler potential.

Contribution

It develops a generic procedure for calculating chiral loop corrections and derives a finite two-loop correction formula for the effective potential in general superfield models.

Findings

Derived a finite two-loop correction formula for the effective potential.

Developed a general method for calculating chiral loop corrections.

Applied the method to models relevant in superstring theory.

Abstract

We study a holomorphic effective potential $W_{eff}(\Phi)$ in chiral superfield model defined in terms of arbitrary k\"{a}hlerian potential $K(\bar{\Phi},\Phi)$ and arbitrary chiral potential $W(\Phi)$. Such a model naturally arises as an ingredient of low-energy limit of superstring theory and it is called here the general chiral superfield model. Generic procedure for calculating the chiral loop corrections to effective action is developed. We find lower two-loop correction in the form $W^{(2)}_{eff}(\Phi)= 6/(4\pi)^4 \bar{W}^{'''2}(0){(\frac{W^{''}(\Phi)}{K^2_{\Phi\bar{\Phi}(0,\Phi)}})}^3$ where $K_{\Phi\bar{\Phi}}(0,\Phi)=\frac{\partial^2 K(\bar{\Phi},\Phi)} {\partial\Phi\partial\bar{\Phi}}|_{\bar{\Phi}=0}$ and $\zeta(x)$ be Riemannian zeta-function. This correction is finite at any $K(\bar{\Phi},\Phi), W(\Phi)$.