The target space depenedence of the Hagedorn temperature

Grignani, G.; Orselli, Marta; Semenoff, Gordon W.

doi:10.1088/1126-6708/2001/11/058

Cited by 10 publications

(28 citation statements)

References 20 publications

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“…exactly as predicted by either the string spectrum A.1 or the divergence in the free energy [10]. We now make a few comments concerning this result.…”

Section: Dominant Hagedorn Behaviorsupporting

confidence: 63%

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Near-Hagedorn thermodynamics and random walks — extensions and examples

Mertens

Verschelde

Захаров

2014

J. High Energ. Phys.

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In this paper, we discuss several explicit examples of the results obtained in [1]. We elaborate on the random walk picture in these spacetimes and how it is modified. Firstly we discuss the linear dilaton background. Then we analyze a previously studied toroidally compactified background where we determine the Hagedorn temperature and study the random walk picture. We continue with flat space orbifold models where we discuss boundary conditions for the thermal scalar. Finally, we study the general link between the quantum numbers in the fundamental domain and the strip and their role in thermodynamics.

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“…exactly as predicted by either the string spectrum A.1 or the divergence in the free energy [10]. We now make a few comments concerning this result.…”

Section: Dominant Hagedorn Behaviorsupporting

confidence: 63%

“…In [10] [11], the authors determine the Hagedorn temperature for a toroidally compactified flat spacetime geometry, when including constant metric and Kalb-Ramond background. This background has applications in non-commutative open string theory [12].…”

Section: Introductionmentioning

confidence: 99%

Near-Hagedorn thermodynamics and random walks — extensions and examples

Mertens

Verschelde

Захаров

2014

J. High Energ. Phys.

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“…Thermodynamical quantities, such as the entropy, diverge at the Hagedorn temperature. If one considers an ensemble of weekly interacting strings at finite temperature, this behavior of the density of states is thought to lead either to a limiting temperature or a phase transition, in which the string configuration changes to one which is dominated by a single long string [32]. The high density Hagedorn phase of matter has been extensively used in cosmology to describe the very early phases of the evolution of the Universe [33]- [36].…”

Section: Introductionmentioning

confidence: 99%

Gravitational collapse of a Hagedorn fluid in Vaidya geometry

Harkó

2003

Phys. Rev. D

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The gravitational collapse of a high-density null charged matter fluid, satisfying the Hagedorn equation of state, is considered in the framework of the Vaidya geometry. The general solution of the gravitational field equations can be obtained in an exact parametric form. The conditions for the formation of a naked singularity, as a result of the collapse of the compact object, are also investigated. For an appropriate choice of the arbitrary integration functions the null radial outgoing geodesic, originating from the shell focussing central singularity, admits one or more positive roots. Hence a collapsing Hagedorn fluid could end either as a black hole, or as a naked singularity. A possible astrophysical application of the model, to describe the energy source of gamma-ray bursts, is also considered.

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“…This is a summary of work which has appeared in a series of publications about this subject, its relationship with the Matrix model of M-theory and related issues, [1]- [5].…”

Section: Preamblementioning

confidence: 99%

DLCQ strings and branched covers of torii

Semenoff

2002

Nuclear Physics B - Proceedings Supplements

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In this lecture I will review some results about the discrete light-cone quantization (DLCQ) of strings and some connections of the results with matrix string theory. I will review arguments which show that, in the path integral representation of the thermal free energy of a string, the compactifications which are necessary to obtain discrete light-cone quantization constrains the integral over all Riemann surfaces of a given genus to the set of those Riemann surfaces which are branched covers of a particular torus. I then review an explicit check of this result at genus 1. I discuss the intriguing suggestion that these branched covers of a torus are related to those which are found in a certain limit of the matrix string model. PreambleIn this lecture I will review some aspects of the discrete light-cone quantization (DLCQ) of strings. This is a summary of work which has appeared in a series of publications about this subject, its relationship with the Matrix model of M-theory and related issues, [1]- [5].One of the essential points will be that, when the light-cone is compactified, the degrees of freedom of the string are thinned somewhat. We will see this by examining the thermodynamic partition function. The thinning of degrees of freedom can be quantified geometrically and summarized in a simple statement about string worldsheets: The set of string worldsheets in DLCQ is the set of those Riemann surfaces which are branched covers of a particular torus, rather than the bigger set of all Riemann surfaces. This means that the string fluctuates less. A further lesson is that these branched covers appear naturally in certain models of random matrices [6]- [12]. The example that we are particularly interested in here is matrix string theory where the limit of weak string * This work is supported in part by NSERC of Canada. coupling of the model is related to string degrees of freedom living on branched covers.After discussing the general result, we will illustrate by doing three different computations of the same quantity: the thermodynamic partition function of discrete light-cone quantized strings. The first computation uses the path Polyakov path integral. The second computation takes the operator quantization of the free string and solves for the spectrum and then constructs the thermodynamic partition function from that spectrum. The third computation begins with a certain limit of the matrix model of M-theory. In this limit the model reduces to a statistical theory of eigenvalues of the matrices which live on branched covers of a torus. The partition function should be compared with that of free type II strings. In all three cases, we obtain an identical result.An essential tool that we use is the thermodynamic partition function. In our case, we simply regard it as a generating function for the energy spectrum of free string theory. Of course, a certain amount of caution must always be used when discussing string theory at finite temperature. Closed string theory is a theory of quantum

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The target space depenedence of the Hagedorn temperature

Cited by 10 publications

References 20 publications

Near-Hagedorn thermodynamics and random walks — extensions and examples

Near-Hagedorn thermodynamics and random walks — extensions and examples

Gravitational collapse of a Hagedorn fluid in Vaidya geometry

DLCQ strings and branched covers of torii

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