Supergravity and Space-Time Non-Commutative Open String Theory

TL;DR

This work uses a dual supergravity description of a near-horizon non-extremal F1-D$p$ bound state to study space-time NCOS theory. It shows that, at leading order, NCOS thermodynamics reproduces ordinary Yang–Mills on a commutative space, while the non-commutative string nature and Hagedorn behaviour emerge only when string corrections or delocalized F-string dynamics are included, particularly near $u_0\sim1$ with very weak coupling. The analysis reveals a phase structure with OYM at low energies ($u\ll R$) and delocalized F-strings at high energies ($u\gg R$), and it clarifies the relationship between NCOS in six dimensions and Little String Theory, predicting distinct Hagedorn temperatures and string scales. The results suggest that NCOS is a low-energy limit of space-time non-commutative LST and motivate further study of string corrections to capture the full thermodynamic behaviour near the NCOS Hagedorn transition.

Abstract

We study the non-critical space-time non-commutative open string (NCOS) theory using a dual supergravity description in terms of a certain near-horizon limit of the F1-Dp bound state. We find the thermodynamics of NCOS theory from supergravity. The thermodynamics is equivalent to Yang-Mills theory on a commutative space-time. We argue that this fact does not have to be in contradiction with the expected Hagedorn behaviour of NCOS theory. To support this we consider string corrections to the thermodynamics. We also discuss the relation to Little String Theory in 6 dimensions.