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We developed a new framework to calculate the Hagedorn temperature for Anti-de Sitter/Conformal Field Theory (AdS/CFT) using integrability. This method determines the Hagedorn temperature for planar N=4 super Yang-Mills theory across all coupling strengths.

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Area of Science:

  • Theoretical Physics
  • String Theory
  • Quantum Field Theory

Background:

  • The Hagedorn temperature signifies a phase transition in quantum systems.
  • Calculating this temperature in Anti-de Sitter/Conformal Field Theory (AdS/CFT) is crucial for understanding quantum gravity.
  • Integrability provides a powerful tool for studying strongly coupled quantum field theories.

Purpose of the Study:

  • To establish a general framework for computing the Hagedorn temperature in AdS/CFT.
  • To derive and solve the thermodynamic Bethe ansatz equations for planar N=4 super Yang-Mills theory.
  • To determine the Hagedorn temperature at various coupling strengths, including previously unknown orders.

Main Methods:

  • Utilizing integrability to derive thermodynamic Bethe ansatz equations.
  • Solving these equations perturbatively at weak coupling using the Y system.
  • Analyzing results at tree level, one-loop, and two-loop orders.

Main Results:

  • A framework for calculating the Hagedorn temperature of AdS/CFT via integrability is established.
  • The thermodynamic Bethe ansatz equations for planar N=4 super Yang-Mills theory are derived.
  • The two-loop Hagedorn temperature is calculated for the first time, confirming previous results at lower orders.

Conclusions:

  • The developed framework provides a systematic way to compute the Hagedorn temperature in AdS/CFT.
  • Integrability is confirmed as an effective tool for studying thermodynamic properties of N=4 super Yang-Mills theory.
  • The results offer insights into the behavior of quantum field theories at finite coupling.