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Nonperturbative conditions for local Weyl invariance on a curved world sheet

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Abstract

We investigate Weyl anomalies on a curved world sheet to second order in a weak field expansion. Using a local version of the exact renormalization group equations, we obtain nonperturbative results for the tachyon/graviton/dilaton system. We discuss the elimination of redundant operators, which play a crucial role for the emergence of target space covariance. Performing the operator product expansion on a curved world sheet allows us to obtain the nonperturbative contributions to the dilaton β function. We find the β functions, after suitable field redefinitions, to be related to a target space effective action through a κ function involving derivatives. Also we can establish a nonperturbative Curci-Paffuti relation including the tachyon β function.

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Author notes

  1. Jens Schnittger

    Present address: Laboratoire de Physique Théorique, Ecole Normale Supérieure, 24 rue Lhomond, F-75231, Paris Cedex 05

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    Authors
    1. Jens Schnittger
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    2. Ulrich Ellwanger
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    Additional information

    Supported by DFG

    Supported by a DFG Heisenberg fellowship.

    Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 2, pp. 361–384, May, 1993.

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    Schnittger, J., Ellwanger, U. Nonperturbative conditions for local Weyl invariance on a curved world sheet. Theor Math Phys 95, 643–662 (1993). https://doi.org/10.1007/BF01017149

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