# 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:

- 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}

}

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