On the stringy nature of winding modes in noncommutative thermal field theories

TL;DR

This paper reveals a duality in thermal noncommutative field theories where non-planar loops are equivalent to exchanges of effective fields resembling closed-string winding modes, connecting field theory and string theory concepts.

Contribution

It introduces a channel duality in thermal noncommutative theories, linking non-planar loops to an infinite tower of effective winding fields akin to closed strings, and clarifies their relation to D-branes.

Findings

Effective winding fields have a closed-string-like mass spectrum.

Winding fields can be interpreted as propagating in a higher-dimensional bulk.

A sum rule relates winding field couplings to closed-string couplings with D-branes.

Abstract

We show that thermal noncommutative field theories admit a version of `channel duality' reminiscent of open/closed string duality, where non-planar thermal loops can be replaced by an infinite tower of tree-level exchanges of effective fields. These effective fields resemble closed strings in three aspects: their mass spectrum is that of closed-string winding modes, their interaction vertices contain extra moduli, and they can be regarded as propagating in a higher-dimensional `bulk' space-time. In noncommutative models that can be embedded in a D-brane, we show the precise relation between the effective `winding fields' and closed strings propagating off the D-brane. The winding fields represent the coherent coupling of the infinite tower of closed-string oscillator states. We derive a sum rule that expresses this effective coupling in terms of the elementary couplings of closed strings to the D-brane. We furthermore clarify the relation between the effective propagating dimension of the winding fields and the true codimension of the D-brane.