Tachyon Effective Dynamics and de Sitter Vacua

TL;DR

This paper reveals a hidden SL(2,R) symmetry in the tachyon DBI action of two-dimensional string theory, interprets it as particles in de Sitter space, and analyzes the collective dynamics and backreaction of branes in this geometric framework.

Contribution

It uncovers a de Sitter space interpretation of the tachyon effective action and develops a collective field theory with geometric insights into brane condensation and backreaction.

Findings

Identification of SL(2,R) symmetry as de Sitter isometries

Formulation of collective field theory in de Sitter space

Calculation of backreaction effects in thermal backgrounds

Abstract

We show that the DBI action for the singlet sector of the tachyon in two-dimensional string theory has a SL(2,R) symmetry, a real-time counterpart of the ground ring. The action can be rewritten as that of point particles moving in a de Sitter space, whose coordinates are given by the value of the eigenvalue and time. The symmetry then manifests as the isometry group of de Sitter space in two dimensions. We use this fact to write the collective field theory for a large number of branes, which has a natural interpretation as a fermion field in this de Sitter space. After spending some time building geometrical insight on facts about the condensation process, the state corresponding to a sD-brane is identified and standard results in quantum field theory in curved space-time are used to compute the backreaction of the thermal background.