One loop scattering on D-branes

TL;DR

This paper computes one-loop scattering amplitudes of massless states on D3-branes using vertex operators, revealing unique divergence structures and exploring potential divergence cancellations via additional vertex operators.

Contribution

It provides a novel analysis of one-loop scattering on D3-branes avoiding D9-brane obstacles, and suggests a connection to non-linear sigma models of D-brane geometry.

Findings

Divergence structure differs from D9-branes due to brane-specific momentum components.

Potential divergence cancellation through added vertex operators.

Link to non-linear sigma models of D-brane/AdS geometry.

Abstract

We analyze one loop scattering amplitudes of the massless states on a stack of D3-branes. We use the vertex operators that have been obtained in the direct open string analysis developed in arXiv:0708.3452. The method does not have the obstacle of the D9 computation which is associated with the appearance of an $\e$-tensor. The divergence structure is not the same as the D9 brane case. What makes the analysis deviate from the D9 brane case is that the momenta of the states have non-zero components only along the brane directions. We ponder on the possibility that the one-loop divergence may be canceled by adding additional vertex operators at the tree level. We anticipate that they will be "exponentiated" to the free string action, with the resulting action to constitute a non-linear sigma model of the D-brane/AdS geometry.