On the effects of the vanishing of the non-metricity to the effective string field equations

TL;DR

This paper revisits effective string field equations, emphasizing the effects of vanishing non-metricity, completing the action density, and deriving the dilaton potential to understand spontaneous Weyl invariance breaking.

Contribution

It provides a complete variational derivation of the action density considering non-metricity effects and unambiguously derives the dilaton potential related to Weyl invariance breaking.

Findings

Completed the action density in the variational setting.

Derived the dilaton potential unambiguously.

Linked vanishing non-metricity to spontaneous Weyl invariance breakdown.

Abstract

Effective string field equations with zero-constrained torsion have been studied extensively in the literature. But, one may think that the effects of vanishing of the non-metricity have not been explained in detail and also in according to some recent literature [4],[5], the action density in my previous paper [3] is not complete. For these reasons, in this erratum, in according to the effects of vanishing of the non-metricity to the field equations, the action density of my previous paper [3] will be completed in a variational setting. Furthermore, up to now, an unambiguous derivation of the dilaton potential has not been given. If one thinks that vanishing of the non-metricity gives a spontaneous breakdown of local Weyl invariance then a dilaton potential is obtained unambiguously in this framework.