Open string radiation from decaying FZZT branes

TL;DR

This paper investigates the decay of unstable FZZT branes using boundary conformal field theory, identifying vertex operators, calculating Bogolyubov coefficients, and analyzing string pair and triplet creation amplitudes.

Contribution

It provides the first explicit computation of vertex operators and pair creation amplitudes in the decay process of FZZT branes within a perturbative framework.

Findings

Identified in- and out- vertex operators for the decay process

Calculated Bogolyubov coefficients relating initial and final states

Derived string pair and triplet creation amplitudes

Abstract

In this paper we continue studying the decay of unstable FZZT branes initiated in [1],[2]. The mass of tachyonic mode in this model can be chosen arbitrarily small and we use it as a perturbative parameter. In [2] a time-dependent boundary conformal field theory (BCFT) describing the decay process was studied and it was shown that in a certain sense this BCFT interpolates between two stationary BCFT's corresponding to the UV and IR fixed points of the associated RG flow. In the present work we find in the leading order vertex operators of the time-dependent BCFT. We identify the "in" and "out" vertex operators assigned to the UV and IR fixed points and compute the related Bogolyubov coefficients. We show that there is a codimension one subspace of the out-going states for which pair creation amplitudes are independent of the initial wave function of the tachyonic mode. We demonstrate that such amplitudes can be computed within the framework of first quantized open string theory via suitably defined string two-point functions. We also evaluate a three point function which we interpret as an amplitude for string triplet creation due to interaction. Some peculiarities of scattering amplitudes in the presence of tachyonic modes in the far past are discussed.