Statistical Entropy of Schwarzschild Black Holes

The entropy of a seven dimensional Schwarzschild black hole of arbitrary large radius is obtained by a mapping onto a near extremal self-dual three-brane whose partition function can be evaluated. The three-brane arises from duality after submitting a neutral blackbrane, from which the Schwarzschild black hole can be obtained by compactification, to an infinite boost in non compact eleven dimensional space-time and then to a Kaluza-Klein compactification. This limit can be defined in precise terms and yields the Bekenstein-Hawking value up to a factor of order one which can be set to be exactly one with the extra assumption of keeping only transverse brane excitations. The method can be generalized to five and four dimensional black holes.Comment: 11 pages, LaTex, no figures, corrected typ

On the Nature of the Hagedorn Transition in NCOS Systems

We extend the study of the nature of the Hagedorn transition in NCOS systems in various dimensions. The canonical analysis results in a microscopic ionization picture of a bound state system in which the Hagedorn transition is postponed till irrelevancy. A microcanonical analysis leads to a limiting Hagedorn behaviour dominated by highly excited, long open strings. The study of the full phase diagram of the NCOS system using the AdS/CFT correspondence suggests that the microscopic ionization picture is the correct one. We discuss some refinements of the ionization mechanism for $d>2$ NCOS systems, including the formation of a temperature-dependent barrier for the process. Some possible consequences of this behaviour, including a potential puzzle for $d=5$, are discussed. Phase diagrams of a regularized form of NCOS systems are introduced and do accomodate a phase of long open strings which disappears in the strict NCOS limit.Comment: 37 pages, 3 Postscript figure

Long time scales and eternal black holes

We discuss the various scales determining the temporal behaviour of correlation functions in the presence of eternal black holes. We point out the origins of the failure of the semiclassical gravity approximation to respect a unitarity-based bound suggested by Maldacena. We find that the presence of a subleading (in the large-N approximation involved) master field does restore the compliance with one bound but additional configurations are needed to explain the more detailed expected time dependence of the Poincare recurrences and their magnitude.Comment: 10 pages, 6 figures. Presented at Johns Hopkins 2003 and Ahrenshoop 2003 workshop

Remarks on Black Hole Instabilities and Closed String Tachyons

Physical arguments stemming from the theory of black-hole thermodynamics are used to put constraints on the dynamics of closed-string tachyon condensation in Scherk--Schwarz compactifications. A geometrical interpretation of the tachyon condensation involves an effective capping of a noncontractible cycle, thus removing the very topology that supports the tachyons. A semiclassical regime is identified in which the matching between the tachyon condensation and the black-hole instability flow is possible. We formulate a generalized correspondence principle and illustrate it in several different circumstances: an Euclidean interpretation of the transition from strings to black holes across the Hagedorn temperature and instabilities in the brane-antibrane system.Comment: harvmac, 20 pp, 4 eps figures. Contribution to Jacob Bekenstein's Festschrif

Touring the Hagedorn Ridge

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.Comment: 29 pages, 18 figures, contribution to I.I. Kogan memorial volume, references adde

On the short-distance structure of irrational non-commutative gauge theories

As shown by Hashimoto and Itzhaki in hep-th/9911057, the perturbative degrees of freedom of a non-commutative Yang-Mills theory (NCYM) on a torus are quasi-local only in a finite energy range. Outside that range one may resort to a Morita equivalent (or T-dual) description appropriate for that energy. In this note, we study NCYM on a non-commutative torus with an irrational deformation parameter $\theta$. In that case, an infinite tower of dual descriptions is generically needed in order to describe the UV regime. We construct a hierarchy of dual descriptions in terms of the continued fraction approximations of $\theta$. We encounter different descriptions depending on the level of the irrationality of $\theta$ and the amount of non-locality tolerated. The behavior turns out to be isomorphic to that found for the phase structure of the four-dimensional Villain $Z_N$ lattice gauge theories, which we revisit as a warm-up. At large 't Hooft coupling, using the AdS/CFT correspondance, we find that there are domains of the radial coordinate $U$ where no T-dual description makes the derivative expansion converge. The radial direction obtains multifractal characteristics near the boundary of AdS.Comment: 17 pages, 4 figures, uses JHEP.cl

Comments on Critical Electric and Magnetic Fields from Holography

We discuss some aspects of critical electric and magnetic fields in a field theory with holographic dual description. We extend the analysis of arxiv:1109.2920, which finds a critical electric field at which the Schwinger pair production barrier drops to zero, to the case of magnetic fields. We first find that, unlike ordinary weakly coupled theories, the magnetic field is not subject to any perturbative instability originating from the presence of a tachyonic ground state in the W-boson spectrum. This follows from the large value of the 't Hooft coupling \lambda, which prevents the Zeeman interaction term to overcome the particle mass at high B. Consequently, we study the next possible B-field instability, i.e. monopole pair production, which is the S-dual version of the Schwinger effect. Also in this case a critical magnetic field is expected when the tunneling barrier drops to zero. These Schwinger-type criticalities are the holographic duals, in the bulk, to the fields E or B reaching the tension of F1 or D1 strings respectively. We then discuss how this effect is modified when electric and magnetic fields are present simultaneously and dyonic states in the spectrum can be pair produced by a generic E - B background. Finally, we analyze finite temperature effects on Schwinger criticalities, i.e. in the AdS-Schwarzshild black hole background.Comment: 33 pages, 4 figures; v2: refs added; v3: typos corrected, to appear on JHE