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tt* Geometry and Closed String Tachyon Potential

Atish Dabholkar, Cumrun Vafa

Open publisher page 53 citations

Abstract

We propose a closed string tachyon action including kinetic and potential terms for non-supersymmetric orbifolds. The action is given in terms of solutions to $tt^*$ equations which captures the geometry of vacua of the corresponding N=2 worldsheet theory. In certain cases the solutions are well studied. In case of tachyons of ${\\bf C}/Z_n$, solutions to affine toda equations determine the action. We study the particular case of ${\\bf C}/Z_3\\to {\\bf C}$ in detail and find that the Tachyon action is determined in terms of a solution to Painleve III equation.

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What this paper is about

We propose a closed string tachyon action including kinetic and potential terms for non-supersymmetric orbifolds. The action is given in terms of solutions to $tt^*$ equations which captures the geometry of vacua of the corresponding N=2 worldsheet theory. In certain cases the solutions are well studied. In case of tachyons of ${\\bf C}/Z_n$, solutions to affine toda equations determine the action. We study the particular case of ${\\bf C}/Z_3\\to {\\bf C}$ in detail and find that the Tachyon action is determined in terms of a solution to Painleve III equation.

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Available abstract

We propose a closed string tachyon action including kinetic and potential terms for non-supersymmetric orbifolds. The action is given in terms of solutions to $tt^*$ equations which captures the geometry of vacua of the corresponding N=2 worldsheet theory. In certain cases the solutions are well studied. In case of tachyons of ${\\bf C}/Z_n$, solutions to affine toda equations determine the action. We study the particular case of ${\\bf C}/Z_3\\to {\\bf C}$ in detail and find that the Tachyon action is determined in terms of a solution to Painleve III equation.

Key concepts: Tachyon, Worldsheet, String (physics), Physics, Action (physics), Mathematical physics, String theory, Tachyon condensation

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