The $SL(K+3,\mathbb{C})$ symmetry of string scatterings from D-branes

TL;DR

This paper demonstrates that string scattering processes involving D-branes at any mass level can be described using a single Lauricella function, revealing an extended $SL(K+3, ext{C})$ symmetry that includes D-branes.

Contribution

It extends the known $SL(K+3, ext{C})$ symmetry of open bosonic string theory to D-brane interactions using Lauricella functions.

Findings

String scattering amplitudes are expressed via Lauricella functions.

The $SL(K+3, ext{C})$ symmetry is extended to include D-branes.

Exact symmetry relations hold at arbitrary mass levels.

Abstract

By using the solvability of Lauricella function $F_{D}^{(K)}\left( \alpha;\beta_{1},...,\beta_{K};\gamma;x_{1},...,x_{K}\right) $ with nonpositive integer $\beta_{J}$, we show that each scattering or decay process of string and D-brane states at \textit{arbitrary} mass levels can be expressed in terms of a single Lauricella function. This result extends the previous exact $SL(K+3,\mathbb{C})$ symmetry of tree-level open bosonic string theory to include the D-brane.