Compactified Strings as Quantum Statistical Partition Function on the Jacobian Torus
arXiv:hep-th/0607133 · doi:10.1103/PhysRevLett.97.261601
Abstract
We show that the solitonic contribution of compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of a compactification in a circle, the Hamiltonian corresponds to the Laplacian on the 2g-dimensional Jacobian torus associated to the genus g Riemann surface corresponding to the string worldsheet. 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 QFT and classical statistical mechanics.
10 pages, typos corrected, minor changes; to appear in Physical Review Letters