Perturbation of the Ground Varieties of C = 1 String Theory

TL;DR

This paper investigates how different types of perturbations affect the structure and singularities of ground rings in c=1 string theory at various compactification radii, revealing conditions under which singularities can be smoothed.

Contribution

It distinguishes the effects of plus-type and minus-type moduli perturbations on ground varieties, showing that only certain perturbations can smoothen singularities.

Findings

Plus-type moduli perturbations do not smoothen singularities.

Minus-type moduli perturbations can lead to semi-universal deformations that smoothen singularities.

Cosmological perturbation can remove singularity only at the self-dual ($A_1$) point.

Abstract

We discuss the effect of perturbations on the ground rings of $c=1$ string theory at the various compactification radii defining the $A_N$ points of the moduli space. We argue that perturbations by plus-type moduli define ground varieties which are equivalent to the unperturbed ones under redefinitions of the coordinates and hence cannot smoothen the singularity. Perturbations by the minus-type moduli, on the other hand, lead to semi-universal deformations of the singular varieties that can smoothen the singularity under certain conditions. To first order, the cosmological perturbation by itself can remove the singularity only at the self-dual ($A_1$) point.}