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Leading infrared logarithms for the σ-model with fields on an arbitrary Riemann manifold

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In memory of Aleksandr Nikolaevich Vasiliev

Abstract

We derive a nonlinear recurrence equation for the infrared leading logarithms (LLs) in the four-dimensional σ-model with fields on an arbitrary Riemann manifold. The derived equation allows computing the LLs to an essentially unlimited loop order in terms of the geometric characteristics of the Riemann manifold. We reduce solving the SU(∞) principal chiral field in an arbitrary number of dimensions in the LL approximation to solving a very simple recurrence equation. This result prepares a way to solve the model in an arbitrary number of dimensions as N → ∞.

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Authors and Affiliations

  1. Konstantinov Petersburg Nuclear Physics Institute, Gatchina, Leningrad Oblast, Russia

    M. V. Polyakov

  2. Institut für Theoretische Physik II, Ruhr-Universität, Bochum, Germany

    M. V. Polyakov & A. A. Vladimirov

Authors
  1. M. V. Polyakov
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  2. A. A. Vladimirov
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Corresponding author

Correspondence to M. V. Polyakov.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 169, No. 1, pp. 158–166, October, 2011.

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Polyakov, M.V., Vladimirov, A.A. Leading infrared logarithms for the σ-model with fields on an arbitrary Riemann manifold. Theor Math Phys 169, 1499–1506 (2011). https://doi.org/10.1007/s11232-011-0126-7

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  • DOI: https://doi.org/10.1007/s11232-011-0126-7

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