Scattering of D0-branes and Strings

TL;DR

The paper addresses infrared divergences in D0-brane scattering with closed strings that arise beyond tree level due to fixed-momentum D0 boundary conditions. It develops a string-field-theory framework that incorporates D0 recoil via collective coordinates, performs a field-redefinition from string fields to collective coordinates, and computes the D0-D0-tachyon amplitude through a carefully regulated annulus contribution. By combining open-string tachyon/ghost treatments, a Jacobian from the field redefinition, and a nonperturbative quantization of the D0 collective modes, the authors obtain a finite, unambiguous amplitude up to first subleading order in the string coupling, with a numerically evaluated annulus term ${\cal F}_{\rm annulus} \approx (1.15900 - 0.43871 i) g_s$. The results demonstrate that infrared issues are resolved within SFT and provide a concrete, regulator-independent prediction for a simple bosonic model, highlighting the importance of recoil and collective-mode dynamics in D-brane scattering.

Abstract

It has been known for about thirty years that a scattering amplitude involving D0-branes and closed strings suffers from infrared divergences beyond tree level. These divergences arise because the conventional world-sheet approach cannot account for the difference between the D0-brane's momentum before and after scattering. We show that, by using string field theory, the divergence can be removed and the amplitude rendered finite and unambiguous. We illustrate this using the simplest possible example in bosonic string theory: a three-point function with one incoming and one outgoing D0-brane and an incoming or outgoing closed string tachyon.

Figures (6)

• Figure 1: This figure shows the Feynman diagrams contributing to the annulus one point function of a closed string. The thick line represents external closed strings and the thin lines denote internal open strings. The interaction vertex with a $\times$ represents part of a disk amplitude, while the interaction vertex with $\otimes$ represents part of an annulus amplitude.
• Figure 2: The moduli space regions associated with the Feynman diagrams shown in Fig. \ref{['figfive']}(a), (b), (c) and (d), as described in eqs.(\ref{['eapp8']})-(\ref{['eapp16']}) in appendix \ref{['scollection']}. The boundaries between different regions shown here are approximate. A more precise description of these boundaries that we use in our analysis can be found in appendix \ref{['scollection']}. This figure is a reproduction of Fig. 8 of 2012.11624 with minor changes.
• Figure 3: This figure shows the Feynman diagram involving internal closed string propagators for the contribution to the annulus one point function from the small $t$ region. The $\times$'s denote interaction vertices associated with disk amplitudes, the thick lines represent closed strings and thin lines represent open strings. The three point interaction vertex in the leftmost diagram is the sphere three point function of three closed strings.
• Figure 4: Additional Feynman diagrams contributing to the annulus one point amplitude. Here $T$ denotes open string tachyon propagator.
• Figure 5: This figure shows two Feynman diagrams contributing to the disk amplitude with one external closed string and two external open strings.