Localized tachyon mass and a g-theorem analogue

TL;DR

This paper investigates localized tachyon condensation in non-supersymmetric orbifolds using mirror Landau-Ginzburg models, revealing an analogy between minimal tachyon mass and c- or g-functions with a monotonicity property.

Contribution

It demonstrates that the minimal tachyon mass in twisted sectors exhibits properties similar to c- and g-functions, establishing a new analogy at the CFT level.

Findings

Minimal tachyon mass satisfies a max property under orbifold decomposition.

c-, g-, and m-functions share a common monotonicity property.

The study reveals an analogy between tachyon mass and known c- and g-functions.

Abstract

We study the localized tachyon condensation (LTC) of non-supersymmetric orbifold backgrounds in their mirror Landau-Ginzburg picture. Using he existence of four copies of (2,2) worldsheet supersymmetry, we show at the CFT level, that the minimal tachyon mass in twisted sectors shows somewhat analogous properties of c- or g-function. Namely, $m := |\alpha' M^2_{min}| $ satisfies $m(M) \geq m(D_1\oplus D_2)={\rm max} \{m(D_1),m(D_2)\}$. $c$- $g$- $m$- functions share the common property $ f(M)\geq f(D_1\oplus D_2)$ for $f=c,g,m$, although they have different behavior in detail.