Toda systems in closed string tachyon condensation

Abstract

We consider $t{t}^{\ast }$ equations appearing in the study of localized tachyon condensations. They are described by various Toda system when we consider the condensation by the lowest tachyon corresponding to the monomial $xy$. The tachyon potential is calculated as a solution to these equations. The Toda system appearing in the deformation of $\C^2/\Z_n$ by $xy$ is identical to that of $D_n$ singularity deformed by $x$. For $\C^3/\Z_n$ with $xyz$ deformation, we find only generic non-simple form, similar to the case appearing in $\C/\Z_5\to \C/\Z_3$ and we discuss the difficulties in these cases.

arXiv comment20 pages, no figure

References in corpus (18)

• Phases of $N=2$ Theories In Two Dimensions
• Don't Panic! Closed String Tachyons in ALE Spacetimes
• A New Supersymmetric Index
• Tachyon Condensation and Black Hole Entropy
• Closed String Tachyon Condensation: An Overview
• Twisted Tachyon Condensation in Closed String Field Theory
• tt* Geometry and Closed String Tachyon Potential
• D-Brane Probe and Closed String Tachyons
• Localized Tachyons and the Quantum McKay Correspondence
• Brane Probes, Toric Geometry, and Closed String Tachyons
• On tachyons, gauged linear sigma models, and flip transitions
• Off-Shell Interactions for Closed-String Tachyons
• Closed String Tachyons and RG flows
• Comments on the Fate of unstable orbifolds
• Tachyon mass, c-function and Counting localized degrees of freedom
• Chiral rings and GSO projection in Orbifolds
• Localized tachyon mass and a g-theorem analogue
• Closed string tachyon potential and $t{t}^{\ast }$ equation