Localized tachyon condensation and G-parity conservation

TL;DR

This paper proves that localized tachyon condensation in non-supersymmetric orbifolds preserves G-parity and increases the lowest tachyon mass squared, confirming a key conjecture in string theory.

Contribution

It demonstrates G-parity preservation during localized tachyon condensation and proves the increase of the lowest tachyon mass squared, confirming a conjecture in type II string theory.

Findings

G-parities of chiral primaries are preserved under CLT

The lowest-tachyon-mass-squared increases under CLT

Equivalence of G-parity definitions from partition function and monomial construction

Abstract

We study the condensation of localized tachyon in non-supersymmetric orbifold ${\C^2/\Z_n}$. We first show that the G-parities of chiral primaries are preserved under the condensation of localized tachyon(CLT) given by the chiral primaries. Using this, we finalize the proof of the conjecture that the lowest-tachyon-mass-squared increases under CLT at the level of type II string with full consideration of GSO projection. We also show the equivalence between the $G$-parity given by $G=[jk_1/n]+ [jk_2/n]$ coming from partition function and that given by $G=\{jk_1/n\}k_2 -\{jk_2/n\}k_1$ coming from the monomial construction for the chiral primaires in the dual mirror picture.