Fields, Strings, Matrices and Symmetric Products

Dijkgraaf, Robbert

doi:10.1007/978-3-322-90172-9_8

Cited by 27 publications

(40 citation statements)

References 52 publications

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“…As is often the case in such computations, it turns to be easier to compute the grand canonical ensemble, i.e. the generating function of the partition functions [10,11,12] …”

Section: Symmetric Orbifoldsmentioning

confidence: 99%

Phase transitions in symmetric orbifold CFTs and universality

Keller

2011

J. High Energ. Phys.

106

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Since many thermodynamic properties of black holes are universal, the thermodynamics of their holographic duals should be universal too. We show how this universality is exhibited in the example of symmetric orbifolds of general two dimensional CFTs. We discuss the free energies and phase diagrams of such theories and show that they are indeed universal in the large N limit. We also comment on the implications of our results for the classification of CFTs that can have an interpretation as holographic duals to gravity theories on AdS

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“…As is often the case in such computations, it turns to be easier to compute the grand canonical ensemble, i.e. the generating function of the partition functions [10,11,12] …”

Section: Symmetric Orbifoldsmentioning

confidence: 99%

Phase transitions in symmetric orbifold CFTs and universality

Keller

2011

J. High Energ. Phys.

106

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“…[17], also cf. [16]) obtained as part of the identification of the elliptic genus of the supersymmetric sigma model of the N-symmetric product of a manifold X and the partition function of a second quantized string theory on X ×S 1 . Namely, in [10] a mathematical proof is given for the following.…”

Section: Definition 34 Let X Be a Variety For Which One Can Define Amentioning

confidence: 99%

Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex

D’Hoker¹,

Phong²,

Yau³

2003

Mirror Symmetry IV

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“…(16), to write the mass-dependent part of eqn. (21) as an operator and take its trace over physical states of the string. This means evaluating the trace over states which obey the level matching condition eqn.…”

Section: Operator Derivation Of the Partition Function For Bosonic Stmentioning

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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Fields, Strings, Matrices and Symmetric Products

Abstract: In these notes we review the role played by the quantum mechanics and sigma models of symmetric product spaces in the light-cone quantization of quantum field theories, string theory and matrix theory.

Cited by 27 publications

References 52 publications

Phase transitions in symmetric orbifold CFTs and universality

Phase transitions in symmetric orbifold CFTs and universality

Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex

DLCQ strings and branched covers of torii

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