Thermal Tachyons and the "g"-Theorem

TL;DR

This paper explains the g-theorem in field and string theory, discusses how vacuum degeneracy g changes under RG flow, and illustrates this with thermal tachyon condensation leading to a lower g vacuum in type II string theory.

Contribution

It clarifies the application of the g-theorem to noncompact sigma models with continuous spectra and demonstrates the lowering of g via thermal tachyon RG flow in string theory.

Findings

Vacuum degeneracy g decreases under RG flow in certain string models.

Thermal tachyon condensation leads to a lower g vacuum state.

The g-theorem applies to noncompact sigma models with continuous spectra.

Abstract

We give a pedagogical introduction to Affleck and Ludwig's g-theorem, distinguishing its applications in field theory vs string theory. We clarify the recent proposal that the vacuum degeneracy $g$ of a noncompact worldsheet sigma model with a continuous spectrum of scaling dimensions is lowered under renormalization group flow while preserving the central charge. As an illustration we argue that the IR stable endpoint of the relevant flow of the worldsheet RG induced by a thermal tachyon in the type II string is the noncompact supersymmetric vacuum with lower $g$. Note Added (Sep 2005).