Touring the Hagedorn Ridge

Abstract

We review aspects of the Hagedorn regime in critical string theories, from basic facts about the ideal gas approximation to the proposal of a global picture inspired by general ideas of holography. It was suggested that the condensation of thermal winding modes triggers a first-order phase transition. We propose, by an Euclidean analogue of the string/black hole correspondence principle, that the transition is actually related to a topology change in spacetime. Similar phase transitions induced by unstable winding modes can be studied in toy models. There, using T-duality of supersymmetric cycles, one can identify a topology change of the Gregory--Laflamme type, which we associate with large-N phase transitions of Yang--Mills theories on tori. This essay is dedicated to the memory of Ian Kogan.

29 pages, 18 figures, contribution to I.I. Kogan memorial volume, references added

References in corpus (3)

• A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
• Thermal Duality Confronts Entropy: A New Approach to String Thermodynamics?
• Thermodynamic nonextensivity in a closed string gas

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• Thermodynamics of Schwarzschild-de Sitter black hole: thermal stability of Nariai black hole
• Accelerating Branes and the String/Black Hole Transition
• Thermal duality and non-singular cosmology in d-dimensional superstrings
• S-brane to thermal non-singular string cosmology
• Random walks and the Hagedorn transition
• Non-singular string cosmology in a 2d Hybrid model
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• Fine structure of Hagedorn transitions
• Phase transition for black holes with scalar hair and topological black holes
• Perturbative String Thermodynamics near Black Hole Horizons
• Geometry And Quantum Noise
• Hagedorn transition and chronology protection in string theory
• The long string at the stretched horizon and the entropy of large non-extremal black holes
• From Free Fields to AdS -- Thermal Case
• Near-Hagedorn Thermodynamics and Random Walks: a General Formalism in Curved Backgrounds
• String Stars in Anti de Sitter Space
• Semi-localized instability of the Kaluza-Klein linear dilaton vacuum
• The Nothing at the Beginning of the Universe Made Precise
• On the Relevance of the Thermal Scalar
• Hedgehog black holes and the Polyakov loop at strong coupling
• The Thermal Scalar and Random Walks in AdS3 and BTZ
• Effective field theory for closed strings near the Hagedorn temperature
• Topology change in commuting saddles of thermal N=4 SYM theory
• Hagedorn divergences and tachyon potential
• Near-Hagedorn Thermodynamics and Random Walks - Extensions and Examples
• String Thermodynamics In and Out of Equilibrium: Boltzmann Equations and Random Walks
• Dark Radiation and the Hagedorn Phase
• Hagedorn String Thermodynamics in Curved Spacetimes and near Black Hole Horizons
• Tachyon condensation and off-shell gravity/gauge duality
• Cosmic superstrings in large volume compactifications: PTAs, LISA and time-varying tension
• Replica trick and string winding
• Fluid Mechanics of Strings
• Size scaling of self gravitating polymers and strings
• Re-Identifying the Hagedorn Transition
• Aspects of String Cosmology
• Matrix Model For Polyakov Loops, String Field Theory In The Temporal Gauge, Winding String Condensation In Anti-de Sitter Space And Field Theory Of D-branes
• On the asymptotic density of states in solvable models of strings
• Renormalization group flows in gauge-gravity duality
• Black Hole Entropy Sourced by String Winding Condensate
• The Hagedorn Temperature and Open QCD-String Tachyons in Pure N=1 Super Yang-Mills
• A correspondence between strings in the Hagedorn phase and asymptotically de Sitter space
• Lectures On AdS-CFT At Weak 't Hooft Coupling At Finite Temperature
• Thermal Equilibrium in String Theory in the Hagedorn Phase
• Entropy of String States at fixed Mass and Size