On the stringy nature of winding modes in non-commutative thermal field theories

We show that thermal non-commutative field theories admit a version of "cha nnel duality" reminiscent of open/closed string duality, where non-planar t hermal loops can be replaced by an infinite tower of tree-level exchanges o f 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 pro pagating in a higher-dimensional "bulk" space-time. In non-commutative mode ls 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-bra ne. The winding fields represent the coherent coupling of the infinite towe r of closed-string oscillator states. We derive a sum rule that expresses t his effective coupling in terms of the elementary couplings of closed strin gs to the D-brane. We furthermore clarify the relation between the effectiv e propagating dimension of the winding fields and the true codimension of t he D-brane.