Closed string tachyon potential and $tt^*$ equation

Details Closed string tachyon potential and $tt^*$ equation Closed string tachyon potential and $tt^*$ equation

2004-12-21

arxiv.org/abs/hep-th/0412247v2

Phys.Lett.B614:113-123,2005

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, reference added. to appear in PLB

Scientific paper

10.1016/j.physletb.2005.03.069

Recently Dabholkar and Vafa proposed that closed string tachyon potential for non-supersymmetric orbifold $\C/\Z_3$ in terms of the solution of a $tt^*$ 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.

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