*-TREK: The One-Loop N=4 Noncommutative SYM Action

TL;DR

This paper analyzes one-loop scattering amplitudes in N=4 noncommutative super Yang-Mills theory, revealing new non-* product structures in nonplanar diagrams and challenges in formulating an off-shell gauge invariant action.

Contribution

It introduces the *_n n-ary operations for nonplanar diagrams and demonstrates the difficulty in constructing an off-shell gauge invariant one-loop effective action.

Findings

Planar diagrams use the usual *-product

Nonplanar diagrams involve additional non-* structures

Off-shell gauge invariance cannot be maintained at one-loop

Abstract

We investigate N=4 noncommutative super Yang-Mills (SYM) theory. We compute the one-loop four gauge boson scattering amplitude on parallel Dp-branes, and find the corresponding contribution to the noncommutative SYM one-loop action in a momentum expansion. The result is somewhat surprising. We find that while the planar diagram can be written using the usual *-product, the contributions from nonplanar diagrams in general involve additional structure beyond the *-product, arising from the nontrivial worldsheet correlations surviving the field theory limit. To each nonplanar diagram, depending on the number n of external vertex operator insertions on each boundary, there is a corresponding *_n n-ary operation. We further find that it is no longer possible to write down an off-shell gauge invariant one-loop effective action using the noncommutative field strength defined at tree-level.