Holographic Hagedorn Temperature: Strong Coupling, Flavor and $\theta$-angle Effects

Abstract

We study the Hagedorn temperature $T_H$ of strongly coupled quantum field theories admitting a holographic string or M-theory description in various regimes and scenarios. In the first part of the paper we propose a ``thermal scalar'' effective approach to the calculation of $T_H$ in eleven-dimensional supergravity. The proposal allows to extend the existing results for $T_H$ to the strongly coupled string regime, i.e. to a previously unexplored regime of field theory parameters where the number of colors $N$ is smaller than (some power of) the 't Hooft coupling $\lambda$. We can thus extend the existing results for the ${\alpha }^{\prime }$ expansion of the ABJM model, which have a spectacular agreement with predictions from integrability, in a different direction in parameter space. In particular, we explicitate the first non-perturbative corrections. We also apply the formalism to the Witten-Yang-Mills model, finding that the result for the ratio of $T_H$ with the deconfinement temperature is in the same ballpark of the lattice one for pure Yang-Mills. Within the same model, we study the dependence of the Hagedorn temperature on the $\theta$-angle. In the second part of the paper we analyze the effect of dynamical flavors on $T_H$ in confining theories. By studying the few available examples of regular backgrounds dual to confining theories with flavors, we find that generally the effects of flavors is to reduce the value of $T_H$ in units of the square root of the confining string tension. The effect turns out to be milder than the analogous reduction of the critical temperature for deconfinement when the latter is known.

arXiv commentLaTeX, 40 pages, 4 figures; v2: comments and clarifications added, typos corrected

References in corpus (27)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Supergravity and a Confining Gauge Theory: Duality Cascades and $\chi$SB-Resolution of Naked Singularities
• Full result for the QCD equation of state with 2+1 flavors
• Thermodynamics of SU(3) Lattice Gauge Theory
• Self Gravitating Fundamental Strings
• Klebanov-Witten theory with massive dynamical flavors
• Axion monodromy in a model of holographic gluodynamics
• Holographic QCD with Dynamical Flavors
• The Klebanov-Strassler model with massive dynamical flavors
• On the gravity dual of Chern-Simons-matter theories with unquenched flavor
• Localized Backreacted Flavor Branes in Holographic QCD
• In search of a Hagedorn transition in SU(N) lattice gauge theories at large-N
• Hagedorn spectrum and thermodynamics of SU(2) and SU(3) Yang-Mills theories
• Notes on Theta Dependence in Holographic Yang-Mills
• On the holographic dual of N=1 SQCD with massive flavors
• The Hagedorn temperature of AdS5/CFT4 via integrability
• The Hagedorn temperature of AdS5/CFT4 at finite coupling via the Quantum Spectral Curve
• Non chiral dynamical flavors and screening on the conifold
• String Stars in Anti de Sitter Space
• Solving the Hagedorn temperature of AdS5/CFT4 via the Quantum Spectral Curve: Chemical potentials and deformations
• Holographic duals of SQCD models in low dimensions
• Higher Order Corrections to the Hagedorn Temperature at Strong Coupling
• Free energy and critical temperature in eleven dimensions
• Semiclassical Quantization of the Superstring and Hagedorn Temperature
• On the Hagedorn Temperature in Holographic Confining Gauge Theories
• Hagedorn temperature in holography: world-sheet and effective approaches
• On the asymptotic density of states in solvable models of strings