Closed Superstring Emission from Rolling Tachyon Backgrounds

TL;DR

This paper calculates the emission of closed superstring states from a decaying unstable D-brane with specific tachyon profiles, revealing divergences in particle production and energy radiation depending on the brane dimension.

Contribution

It provides a direct path integral computation of the boundary state for superstring tachyon profiles and relates string emission to group integrals over $U(n) imes U(m)$, extending previous bosonic results.

Findings

Total particle production diverges for D0-branes.

Energy radiated diverges for Dp-branes with p ≤ 2.

Method relates boundary states to $U(n) imes U(m)$ integrals.

Abstract

We compute the lowest components of the Type II Ramond-Ramond boundary state for the tachyon profile $T (X) = \lambda e ^{X ^ 0/\sqrt{2}}$ by direct path integral evaluation. The calculation is made possible by noting that the integrals involved in the requisite disk one-point functions reduce to integrals over the product group manifold $U (n)\times U (m)$. We further note that one-point functions of more general closed string operators in this background can also be related to $U (n)\times U (m)$ group integrals. Using this boundary state, we compute the closed string emission from a decaying unstable D$p$-brane of Type II string theory. We also discuss closed string emission from the tachyon profile $T (X) =\lambda\cosh (X ^ 0/\sqrt{2})$. We find in both cases that the total number of particles produced diverges for $p = 0$, while the energy radiated into closed string modes diverges for $p\leq 2$, in precise analogy to the bosonic case.