Matrix Theory Interpretation of Discrete Light Cone Quantization String Worldsheets

Grignani, G.; Orland, Peter; Paniak, L. D.; Semenoff, Gordon W.

doi:10.1103/physrevlett.85.3343

Cited by 25 publications

(46 citation statements)

References 13 publications

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“…(5.18) and (5.23) there), has been subsequently and independently derived in [5] by studying the null compactification of type-IIA-string perturbation theory at finite temperature. In [5] an equivalent proof of Theorem 3 is also provided.…”

Section: Theorem 2 If the Holomorphic One-differentials ω Nm And ω mentioning

confidence: 99%

Eigenfunctions of the Laplacian acting on degree zero bundles over special Riemann surfaces

Matone

2004

Trans. Amer. Math. Soc.

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Abstract. We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces of genus greater than one. These special surfaces correspond to Riemann period matrices satisfying a set of equations which lead to a number theoretical problem. It turns out that these surfaces precisely correspond to branched covering of the torus. This reflects in a Jacobian with a particular kind of complex multiplication.

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Section: Theorem 2 If the Holomorphic One-differentials ω Nm And ω mentioning

confidence: 99%

Eigenfunctions of the Laplacian acting on degree zero bundles over special Riemann surfaces

Matone

2004

Trans. Amer. Math. Soc.

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“…It is interesting to ask whether one can characterize this subset in a convenient way. In this Section we will review a theorem about the classification which was proved in [2]. A hint about this classification can be found by counting the number of moduli of the Riemann surface that eqn.…”

Section: Type II Superstring At Genusmentioning

confidence: 99%

“…This result was first obtained in ref. [2]. Since the first homology group of the 2-sphere is trivial, the first order in perturbation theory which is affected is at genus 1.…”

Section: Dlcq Of the String: Path Integralmentioning

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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“…This equivalence may be given a geometric interpretation by introducing a finite temperature [31,33]. This is done by further compactifying Euclidean time so that two target space directions are compactified on a torus T 2 τ of a particular modulus τ .…”

Section: Introductionmentioning

confidence: 99%

“…For the present discussion, the thermodynamic partition function is simply regarded as a generating function for the energy spectrum of free string theory and thermal instabilities such as the gravitational Jeans instability or the stringy Hagedorn transition will be ignored. On the Type IIA side, the one-loop free energy is given by a sum over unramified coverings of the torus T 2 τ of degree N [31,33]. On the superconformal field theory side, the partition function on T 2 τ is given by a sum over twisted sectors imposing S N -twisted boundary conditions on the string embedding fields.…”

Section: Introductionmentioning

confidence: 99%

Two-loop string theory on null compactifications

Cove

Szabo

2006

Nuclear Physics B

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We compute the two-loop contributions to the free energy in the null compactification of perturbative string theory at finite temperature. The cases of bosonic, Type II and heterotic strings are all treated. The calculation exploits an explicit reductive parametrization of the moduli space of infinite-momentum frame string worldsheets in terms of branched cover instantons. Various arithmetic and physical properties of the instanton sums are described. Applications to symmetric product orbifold conformal field theories and to the matrix string theory conjecture are also briefly discussed.

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Matrix Theory Interpretation of Discrete Light Cone Quantization String Worldsheets

Cited by 25 publications

References 13 publications

Eigenfunctions of the Laplacian acting on degree zero bundles over special Riemann surfaces

Eigenfunctions of the Laplacian acting on degree zero bundles over special Riemann surfaces

DLCQ strings and branched covers of torii

Two-loop string theory on null compactifications

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