F^5 contributions to the nonabelian Born Infeld action from a supersymmetric Yang-Mills five-point function

TL;DR

This paper computes one-loop five-point functions in N=4 supersymmetric Yang-Mills theory to determine the structure of F^5 terms in the nonabelian Born-Infeld action, highlighting the importance of both symmetric and antisymmetric derivative contributions.

Contribution

It provides the first detailed calculation of five-point functions to inform the nonabelian F^5 terms in the Born-Infeld action, including derivative contributions beyond the symmetrized trace.

Findings

Identified the structure of F^5 terms in the nonabelian Born-Infeld action.

Showed the necessity of including both symmetric and antisymmetric derivative contributions.

Compared field theory results with open superstring theory calculations.

Abstract

We consider the N=4 supersymmetric Yang-Mills theory in four dimensions. We compute the one-loop contributions to the effective action with five external vector fields and compare them with corresponding results in open superstring theory. Our calculation determines the structure of the F^5 terms that appear in the nonabelian generalization of the Born Infeld action. The trace operation on the gauge group indices receives contributions from the symmetric as well as the antisymmetric part. We find that in order to study corrections to the symmetrized trace prescription one has to consistently take into account derivative contributions not only with antisymmetrized products \nabla_{[\mu}\nabla_{\nu]} but also with symmetrized ones \nabla_{(\mu}\nabla_{\nu)}.