TY - JOUR

T1 - Modular invariance and stochastic quantization

AU - Ordez, Carlos R.

AU - Rubin, Mark A.

AU - Zwanziger, Daniel

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1989

Y1 - 1989

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevD.40.4056

DO - 10.1103/PhysRevD.40.4056

M3 - Article

AN - SCOPUS:35949012189

VL - 40

SP - 4056

EP - 4072

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 12

ER -