Modular invariance and stochastic quantization

Carlos R. Ordez, Mark A. Rubin, Daniel Zwanziger

    Research output: Contribution to journalArticle


    In Polyakov path integrals and covariant closed-string field theory, integration over Teichmüller parameters must be restricted by hand to a single modular region. This problem has an analog in Yang-Mills gauge theorynamely, the Gribov problem, which can be resolved by the method of stochastic gauge fixing. This method is here employed to quantize a simple modular-invariant system: the Polyakov point particle. In the limit of a large gauge-fixing force, it is shown that suitable choices for the functional form of the gauge-fixing force can lead to a restriction of Teichmüller integration to a single modular region. Modifications which arise when applying stochastic quantization to a system in which the volume of the orbits of the gauge group depends on a dynamical variable, such as a Teichmüller parameter, are pointed out, and the extension to Polyakov strings and covariant closed-string field theory is discussed.

    Original languageEnglish (US)
    Pages (from-to)4056-4072
    Number of pages17
    JournalPhysical Review D
    Issue number12
    StatePublished - 1989

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)

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    Ordez, C. R., Rubin, M. A., & Zwanziger, D. (1989). Modular invariance and stochastic quantization. Physical Review D, 40(12), 4056-4072.