Non-orientable string one-loop corrections in the presence of a B field

TL;DR

This paper derives the string propagator on a Möbius strip with a B field and uses it to compute one-loop corrections in noncommutative SO(N) gauge theories, confirming their consistency with known field theory results.

Contribution

It provides a new expression for the string propagator on the Möbius strip with a B field and applies it to compute one-loop gluon amplitudes in noncommutative SO(N) gauge theories.

Findings

One-loop corrections match noncommutative SO(N) gauge theory predictions.

Derived the string propagator on the Möbius strip with B field.

Confirmed compatibility between string and field theory results.

Abstract

We discuss the problem of noncommutative SO(N) gauge field theories from the string one-loop point of view. To this end we propose an expression for the string propagator on the boundary of the Moebius strip in the presence of a constant B field. We discuss in detail the problems related to its derivation. Then we use it to compute the one-loop corrections to two-, three- and four-gluon amplitudes in an open string theory with orthogonal Chan-Paton factors. We show that these corrections in the field theory limit in 4D are compatible with the one-loop corrections of a renormalizable noncommutative SO(N) gauge field theory.