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Thermal Duality and the Canonical String Ensemble

Year: 2004
Type: preprint
Abstract: We give a first principles formulation of equilibrium string thermodynamics in the canonical ensemble, compatible with the Euclidean timelike T-duality transformations that link the six supersymmetric string theories in pairs: heterotic E8xE8 and Spin(32)/Z2, type IIA and type IIB, or type IB and type I'. Starting with the heterotic string, we explain why the requirement that the finite temperature vacuum energy density interpolate smoothly between distinct supersymmetric string ground states at zero and infinite temperature removes the tachyonic thermal instabilities present in all previous attempts to formulate an equilibrium heterotic string thermodynamics. Likewise, in the type I and type II string theories, we find that in the presence of Dbranes, and a consequent Yang-Mills gauge sector, the canonical ensemble is indeed infrared stable, with neither tachyons nor massless scalar tadpoles. We demonstrate that the full string ensemble in each case exhibits a strong version of holography, as originally conjectured by Atick and Witten in 1988, and shown for the closed bosonic string by Polchinski in 1998. We establish that the thermal duality transition lies within the Kosterlitz-Thouless universality class, verifying also that the low energy limit of our string results reproduce the expected growth in the number of degrees of freedom in a 10D finite temperature field theory. In closing, we give evidence that the pair correlator of timelike Wilson loops is an order parameter for a first order phase transition in the low energy gauge theory to a long string phase at temperatures above the string scale. Remarkably, the thermal dual type I' description enables precise computations to be made in the long string phase.
Language: English
Open Access status: green
OpenAlex ID: W2803357720
Cites: 18
Cited by: 1
Related to: 10