[Paper Review] Thermal Duality and the Canonical String Ensemble

Shyamoli Chaudhuri|arXiv (Cornell University)|Sep 29, 2004

Black Holes and Theoretical PhysicsPhysics and Astronomy18 references1 citations

TL;DR

This paper formulates equilibrium string thermodynamics in the canonical ensemble using thermal duality to resolve tachyonic instabilities in heterotic strings and ensure infrared stability in type I/II strings with D-branes. It establishes a strong holographic principle, identifies the thermal duality transition as Kosterlitz-Thouless class, and shows that timelike Wilson loop pair correlators act as order parameters for a first-order phase transition into a long string phase, with precise computations possible via thermal dual type I' description.

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.

Motivation & Objective

• To resolve long-standing tachyonic thermal instabilities in heterotic string thermodynamics using thermal duality.
• To establish infrared stability in type I and type II string theories by incorporating D-branes and Yang-Mills sectors.
• To demonstrate that the full string ensemble exhibits a strong form of holography, as conjectured by Atick and Witten.
• To identify the universality class of the thermal duality transition and confirm consistency with 10D finite-temperature field theory.
• To identify the pair correlator of timelike Wilson loops as an order parameter for a first-order phase transition into the long string phase.

Proposed method

• Constructs a first-principles formulation of equilibrium string thermodynamics in the canonical ensemble using Euclidean timelike T-duality.
• Applies thermal duality to ensure smooth interpolation of vacuum energy density between zero and infinite temperature limits, removing tachyonic instabilities.
• Incorporates D-branes and Yang-Mills gauge sectors to stabilize the infrared regime in type I and type II strings.
• Uses holographic duality to connect the full string ensemble to a dual field theory, verifying consistency with 10D finite-temperature field theory.
• Analyzes the thermal duality transition using renormalization group techniques, placing it in the Kosterlitz-Thouless universality class.
• Identifies the pair correlator of timelike Wilson loops as a non-perturbative order parameter for the phase transition to the long string phase.

Experimental results

Research questions

• RQ1 How can tachyonic instabilities in heterotic string thermodynamics be resolved within a canonical ensemble framework?
• RQ2 What role do D-branes and Yang-Mills sectors play in ensuring infrared stability in type I and type II string theories?
• RQ3 Does the full string ensemble exhibit a strong form of holography, as proposed by Atick and Witten?
• RQ4 To which universality class does the thermal duality transition belong, and how does it relate to known field theory behavior?
• RQ5 Can the pair correlator of timelike Wilson loops serve as an order parameter for a first-order phase transition into the long string phase?

Key findings

• The requirement of smooth vacuum energy interpolation across temperature scales eliminates tachyonic instabilities in the heterotic string, ensuring thermal stability.
• In the presence of D-branes and Yang-Mills sectors, the type I and type II string theories are infrared stable, with no tachyons or massless scalar tadpoles.
• The full string ensemble exhibits a strong version of holography, consistent with the Atick-Witten conjecture and Polchinski’s earlier results for the bosonic string.
• The thermal duality transition is shown to lie within the Kosterlitz-Thouless universality class, confirming its critical behavior.
• The low-energy limit of the string results correctly reproduce the expected growth in the number of degrees of freedom in 10D finite-temperature field theory.
• The pair correlator of timelike Wilson loops is identified as a non-perturbative order parameter for a first-order phase transition into the long string phase, with the thermal dual type I' description enabling precise computations in this phase.