N-point functions in rolling tachyon background

TL;DR

This paper computes boundary correlation functions in Timelike Boundary Liouville theory, providing exact one-point functions, exploring their properties, and deriving a new asymptotic approximation for Toeplitz determinants relevant for string theory.

Contribution

It presents an exact one-point function in Timelike Boundary Liouville theory and introduces a novel asymptotic approximation for Toeplitz determinants, connecting to string theory.

Findings

Exact one-point function consistent with conserved charges

Explicit n-point tachyon amplitude expression

New asymptotic approximation for Toeplitz determinants

Abstract

We study n-point boundary correlation functions in Timelike Boundary Liouville theory, relevant for open string multiproduction by a decaying unstable D-brane. We give an exact result for the one-point function of the tachyon vertex operator and show that it is consistent with a previously proposed relation to a conserved charge in string theory. We also discuss when the one-point amplitude vanishes. Using a straightforward perturbative expansion, we find an explicit expression for a tachyon n-point amplitude for all n, however the result is still a toy model. The calculation uses a new asymptotic approximation for Toeplitz determinants, derived by relating the system to a Dyson gas at finite temperature.