Rolling Tachyons from Liouville theory

TL;DR

This paper provides an exact solution for the c=1 Liouville model describing homogeneous decay of a closed string tachyon, revealing two distinct theories with different signatures and non-analytic amplitudes.

Contribution

It introduces a novel exact solution for the c=1 Liouville theory and explores the differences between Euclidean and Lorentzian signatures in tachyon decay.

Findings

Two distinct c=1 Liouville theories with different signatures

Non-analytic behavior of amplitudes in c=1 models

Euclidean limit matches Runkel and Watts' interacting c=1 theory

Abstract

In this work we propose an exact solution of the c=1 Liouville model, i.e. of the world-sheet theory that describes the homogeneous decay of a closed string tachyon. Our expressions are obtained through careful extrapolation from the correlators of Liouville theory with c > 25. In the c=1 limit, we find two different theories which differ by the signature of Liouville field. The Euclidean limit coincides with the interacting c=1 theory that was constructed by Runkel and Watts as a limit of unitary minimal models. The couplings for the Lorentzian limit are new. In contrast to the behavior at c > 1, amplitudes in both c=1 models are non-analytic in the momenta and consequently they are not related by Wick rotation.