Miracle at the Gepner Point

TL;DR

This paper computes a specific four-point function in a string theory context, demonstrating the flatness of the superpotential at a certain order, which informs the understanding of (0,2) moduli space deformations.

Contribution

It provides an analytic and numerical calculation of a four-point function related to (0,2) deformations of the quintic string vacuum, revealing superpotential flatness.

Findings

The four-point function satisfies conformal and monodromy conditions.

The integrated amplitude vanishes, indicating superpotential flatness.

Results contribute to understanding the (0,2) moduli space and superpotential.

Abstract

A four-point function of $E_6$ singlets, of interest in elucidating the moduli space of (0,2) deformations of the quintic string vacuum, is computed using analytic and numerical methods. The conformal field theory amplitude satisfies the requisite selection rules and monodromy conditions, but the integrated string amplitude vanishes. Together with selection rules coming from the spacetime R-symmetry \dksecond, this demonstrates the flatness of the gauge-singlet spacetime superpotential through fourth order. Relevance to the more general program of determining the (0,2) moduli space and superpotential is discussed.