O(D) invariant tachyon condensates in the 1/D expansion

TL;DR

This paper analyzes O(D) symmetric open string tachyon condensates using a 1/D expansion, revealing that only polynomial tachyon fields are consistent and providing exact potentials for quadratic profiles.

Contribution

It introduces an exactly solvable large D limit for symmetric tachyon condensation and derives the exact quadratic tachyon potential, improving previous approximate methods.

Findings

1. 1/D expansion is consistent only for polynomial tachyon fields.

2. The theory is renormalized by normal ordering the interaction.

3. Exact quadratic tachyon potential is derived.

Abstract

We consider the problem of condensation of open string tachyon fields which have an O(D) symmetric profile. This problem is described by a boundary conformal field theory with D scalar fields on a disc perturbed by relevant boundary operators with O(D) symmetry. The model is exactly solvable in the large D limit and we analyze its 1/D expansion. We find that this expansion is only consistent for tachyon fields which are polynomials. In that case, we show that the theory is renormalized by normal ordering the interaction. The beta-function for the tachyon field is the linear wave operator. We derive an expression for the tachyon potential and compare with other known expressions. In particular, our technique gives the exact potential for the quadratic tachyon profile. It can be used to correct the action which has been derived in that case iteratively in derivatives of the tachyon field.