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Title: Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus

Abstract

We show that the solitonic contribution of toroidally compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of compactification on a circle, the Hamiltonian is the Laplacian on the 2g-dimensional Jacobian torus associated with the genus g Riemann surface corresponding to the string world sheet. T duality leads to a symmetry of the partition function mixing time and temperature. Such a classical-quantum correspondence and T duality shed some light on the well-known interplay between time and temperature in quantum field theory and classical statistical mechanics.

Authors:
; ; ;  [1]
  1. Dipartimento di Fisica 'G. Galilei' and Istituto Nazionale di Fisica Nucleare, Universita di Padova, Via Marzolo, 8-35131 Padova (Italy)
Publication Date:
OSTI Identifier:
20861536
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 97; Journal Issue: 26; Other Information: DOI: 10.1103/PhysRevLett.97.261601; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPACTIFICATION; DUALITY; HAMILTONIANS; LAPLACIAN; PARTITION FUNCTIONS; QUANTUM FIELD THEORY; RIEMANN SHEET; STATISTICAL MECHANICS; STRING MODELS; SYMMETRY

Citation Formats

Matone, Marco, Pasti, Paolo, Shadchin, Sergey, and Volpato, Roberto. Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus. United States: N. p., 2006. Web. doi:10.1103/PHYSREVLETT.97.261601.
Matone, Marco, Pasti, Paolo, Shadchin, Sergey, & Volpato, Roberto. Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus. United States. doi:10.1103/PHYSREVLETT.97.261601.
Matone, Marco, Pasti, Paolo, Shadchin, Sergey, and Volpato, Roberto. Sun . "Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus". United States. doi:10.1103/PHYSREVLETT.97.261601.
@article{osti_20861536,
title = {Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus},
author = {Matone, Marco and Pasti, Paolo and Shadchin, Sergey and Volpato, Roberto},
abstractNote = {We show that the solitonic contribution of toroidally compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of compactification on a circle, the Hamiltonian is the Laplacian on the 2g-dimensional Jacobian torus associated with the genus g Riemann surface corresponding to the string world sheet. T duality leads to a symmetry of the partition function mixing time and temperature. Such a classical-quantum correspondence and T duality shed some light on the well-known interplay between time and temperature in quantum field theory and classical statistical mechanics.},
doi = {10.1103/PHYSREVLETT.97.261601},
journal = {Physical Review Letters},
number = 26,
volume = 97,
place = {United States},
year = {Sun Dec 31 00:00:00 EST 2006},
month = {Sun Dec 31 00:00:00 EST 2006}
}
  • In this paper the authors consider the interrelation between compactified string theories on torus and gauge fields on it. The authors start from open string theories with background gauge fields and derive partition functions by path integral. Since the effects of background fields and compactification correlate only through string zero modes, we investigate these zero modes. From this point of view, the authors discuss the Wilson loop mechanism at finite temperature. For the closed string, only a few comments are mentioned.
  • The partition function of the bosonic string compactified on a singular orbifold is derived. All the information about the orbifold structure is contained in the combination of theta functions specific to it, in terms of which the partition function is expressed.
  • The modular measure corresponding to the contribution to the string partition function from the surface with {ital n} handles and {ital m}+1 holes is calculated.
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