Closed string tachyon potential and $t{t}^{\ast }$ equation

Abstract

Recently Dabholkar and Vafa proposed that closed string tachyon potential for non-supersymmetric orbifold $\C/\Z_3$ in terms of the solution of a $t{t}^{\ast }$ equation. We extend this result to $\C^2/\Z_n$ for $n=3,4,5$. Interestingly, the tachyon potentials for $n=3$ and 4 are still given in terms of the solutions of Painleve III type equation that appeared in the study of $\C^1/\Z_3$ with different boundary conditions. For $\C^2/\Z_5$ case, governing equations are of generalized Toda type. The potential is monotonically decreasing function of RG flow.

15 pages, reference added. to appear in PLB

References in corpus (6)

• Twisted Tachyon Condensation in Closed String Field Theory
• Localized Tachyons and the Quantum McKay Correspondence
• On tachyons, gauged linear sigma models, and flip transitions
• Comments on the Fate of unstable orbifolds
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Cited by in corpus (1)

• Toda systems in closed string tachyon condensation