Deconfinement and the Hagedorn transition in string theory

Area of Science:

• String Theory
• Quantum Field Theory
• High-Energy Physics

Background:

• The behavior of string theories at finite temperatures is crucial for understanding their dualities.
• Existing definitions of thermal partition functions have limitations in describing these dualities comprehensively.

Purpose of the Study:

• To introduce a novel definition for the thermal partition function in string theory.
• To explore the implications of this new definition on thermal duality relations and phase transitions.

Main Methods:

• A new definition of the thermal partition function was formulated.
• A beta-->beta(2)(H)/beta transformation was applied to type I string theory.
• The behavior of static heavy quark-antiquark potentials was analyzed.

Main Results:

• All string theories exhibit thermal duality relations with a self-dual Hagedorn temperature.
• A new string theory (type I) with thermal D p-branes was derived.
• A continuous phase transition was observed in the heavy quark-antiquark potential, following an inverse power law at a critical temperature.

Conclusions:

• The new definition unifies the understanding of thermal properties across different string theories.
• The findings provide insights into the non-Abelian Higgs-gauge theory on thermal D p-branes.
• The identified phase transition offers a new perspective on the behavior of matter at extreme temperatures within string theory frameworks.