One-dimensional string theory on a circle

David J. Gross, Igor Klebanov

Research output: Contribution to journalArticlepeer-review

203 Scopus citations


We discuss random matrix-model representations of D = 1 string theory, with particular emphasis on the case in which the target space is a circle of finite radius. The duality properties of discretized strings are analyzed and shown to depend on the dynamics of vortices. In the representation in terms of a continuous circle of matrices we find an exact expression for the free energy, neglecting non-singlet states, as a function of the string coupling and the radius which exhibits exact duality. In a second version, based on a discrete chain of matrices, we find that vortices induce, for a finite radius, a Kosterlitz-Thouless phase transition that takes us to a c = 0 theory.

Original languageEnglish (US)
Pages (from-to)475-498
Number of pages24
JournalNuclear Physics, Section B
Issue number3
StatePublished - Nov 19 1990

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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