Condensation de tachyon dans le syst\`eme brane-antibrane

TL;DR

This paper investigates tachyon condensation in brane-antibrane systems within superstring theory, demonstrating the limitations of existing effective actions and establishing a consistent conformal field theory description for the entire tachyonic domain.

Contribution

It proves the existence of a conformal field theory for the full tachyonic domain and derives a quadratic effective action consistent with the RG flow and equations of motion.

Findings

Confirmed the CFT exists across the entire tachyonic domain.

Validated the quadratic effective action through RG analysis.

Showed the limitations of Garousi's effective action for time-dependent tachyon condensation.

Abstract

In superstring theory of type II, the separated brane-antibrane pair admits a bi-fundamental tachyon in its open string spectrum, for any separation less than the critical distance. The dynamics of this system would be described by the Garousi's effective action for any non-zero separation. Our study shows however that the domain of validity of this action only includes space-like tachyon condensation. Previous studies led by Bagchi and Sen showed that, in a partial sub-critical domain, exists a conformal field theory (CFT), which describes a dynamical condensation at static distance, called rolling tachyon. We show that this CFT actually exists on the whole tachyonic domain. Thanks to this demonstration, we prove that the domain of validity of Garousi's action excludes time-dependent tachyon condensation, and we justify the computation of the partition fonction along the rolling tachyon on the whole sub-critical domain. Using a method proposed by Kutasov and Niarchos, we determine a quadratic effective action for the tachyon and distance fields, at least valid in the whole tachyonic domain around the rolling tachyon solution. In addition, we studied the non linear sigma model of perturbative deformations along the rolling tachyon CFT. The beta-function of the renormalization group, that we obtained, are in good agreement with the equations of movement derived from the proposed quadratic effective action. This stands as an independent confirmation of its expression.