On the Production of Open Strings from Brane Anti-Brane Annihilation

TL;DR

The paper tackles the challenge of open-string production in the time-dependent Dar{D} background by analyzing the leading 1-loop open-string contribution with BCFT methods. It demonstrates that naive expansions of Sen's boundary state in oscillator levels yield late-time divergences, but a full sum over oscillator levels and momenta in the Euclidean theory followed by the correct inverse Wick rotation produces a finite amplitude. Through partial summation and explicit structure in the rolling tachyon boundary state, it connects to Li_2-type expressions and argues for the finiteness of the 1-loop open-string channel, while conjecturing general forms for 1-point and 2-point amplitudes and discussing the relative significance of open versus closed string production for reheating in brane inflation. The work provides a methodological framework and highlights the need for a complete boundary-state expansion to firmly determine open-string production and its impact on cosmological reheating, with implications for phase-space considerations and SU(2) symmetry in the boundary state. Overall, it advances understanding of 1-loop open-string dynamics in time-dependent backgrounds and establishes a pathway to quantify open-string versus closed-string production in brane inflation scenarios.

Abstract

We investigate the leading contribution to open string production in the time dependent background of the Brane Anti-Brane. This is a 1-loop diagram and we use Boundary Conformal Field Theory (BCFT) techniques to study it. We show that the amplitude to a single open string naively diverges when one looks at it as an expansion in oscillator levels. Nevertheless, we show that once we sum over all oscillator levels we get a finite result. We also clarify where to perform the inverse Wick rotation in this kind of problems. This calculation could have important consequences for the theory of reheating in brane inflationary models.

Figures (6)

• Figure 1: Disc diagram with insertion of a closed string vertex operator (this is of order $g_s^0$).
• Figure 2: $\text{D}\bar{\text{D}}$ (large white circle) emitting the fields $S$ and $S^\dagger$ that then annihilates on a spectator brane to produce a gauge field $A$.
• Figure 3: 1-point function on the cylinder where one end (dashed line) represents the $\text{D}\bar{\text{D}}$ time dependent source and the other end represents the spectator brane.
• Figure 4: 2-point function on the cylinder where one end (dashed line) represents the $\text{D}\bar{\text{D}}$ time dependent source and the other end represents the spectator brane.
• Figure 5: Next to next leading order correction to brane decays.