[Paper Review] Open String Creation by S-Branes

Andrew Strominger|ArXiv.org|Sep 10, 2002

Black Holes and Theoretical Physics20 references97 citations

TL;DR

This paper investigates open string pair creation by an unstable s-brane using a minisuperspace approximation of boundary Liouville theory. It finds a Hagedorn-like divergence in the pair creation rate due to an exponentially growing density of high-energy open string states, suggesting rapid energy transfer to closed strings, and implies the $g_s \to 0$ limit is non-smooth in this approximation.

ABSTRACT

An sp-brane can be viewed as the creation and decay of an unstable D(p+1)-brane. It is argued that the decaying half of an sp-brane can be described by a variant of boundary Liouville theory. The pair creation of open strings by a decaying s-brane is studied in the minisuperspace approximation to the Liouville theory. In this approximation a Hagedorn-like divergence is found in the pair creation rate, suggesting the s-brane energy is rapidly transferred into closed string radiation.

Motivation & Objective

• To understand time-dependent tachyon decay on an unstable D(p+1)-brane via s-brane dynamics.
• To analyze open string production in the half-s-brane background using a minisuperspace approximation.
• To assess the validity of the $g_s \to 0$ limit in string perturbation theory for s-brane decay.
• To determine whether open string pair creation leads to strong coupling and energy transfer to closed strings.

Proposed method

• Adapts the minisuperspace approximation from Liouville theory to model time-dependent open string masses on a half-s-brane.
• Models the tachyon background as generating exponentially growing open string masses via $m^2(X^0) \propto e^{X^0/\sqrt{\alpha'}}$.
• Uses a boundary Liouville theory with $e^{X^0}$ interaction to describe the decaying half of the s-brane.
• Computes the open string creation rate using a scalar field with exponential mass growth, analogous to Hagedorn behavior.
• Estimates the total energy in produced open strings via $\int N_\omega d\mathcal{E}_\omega$, with $N_\omega \sim \omega^{-a} e^{\omega/T_H}$.
• Analyzes the divergence of the integral at high energies, linked to the Hagedorn temperature $T_H = 1/(4\pi\sqrt{\alpha'})$.

Experimental results

Research questions

• RQ1 Does open string pair creation by a decaying s-brane lead to a divergent production rate in the minisuperspace approximation?
• RQ2 What is the role of the Hagedorn temperature in the open string creation process on a half-s-brane?
• RQ3 How does the $g_s \to 0$ limit affect the validity of perturbative string theory in describing s-brane decay?
• RQ4 Can the divergent open string production rate be suppressed by increasing the number of non-compact transverse dimensions?
• RQ5 Is the energy of the s-brane rapidly transferred into closed string radiation due to strong coupling from open string production?

Key findings

• The open string pair creation rate diverges due to a high-energy density of states scaling as $\omega^{-a} e^{\omega/T_H}$, where $a$ is the number of non-compact transverse dimensions.
• The divergence is analogous to Hagedorn behavior, suggesting the system attempts to produce open strings at the Hagedorn temperature $T_H = 1/(4\pi\sqrt{\alpha'})$.
• The divergence implies that the linearized approximation breaks down at a finite time $t_C$, independent of $g_s$, due to strong coupling from open string production.
• Even for small $g_s$, the system becomes strongly coupled before $t_C$, invalidating perturbative analysis and suggesting rapid energy transfer to closed strings.
• The $g_s \to 0$ limit is not smooth in the minisuperspace approximation, as the divergence persists and signals a breakdown of perturbation theory.
• The final state is likely dominated by closed string radiation, despite formal decoupling in the $g_s \to 0$ limit.