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On duality symmetry in perturbative quantum theory

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Abstract

Non-compact symmetries of extended 4d supergravities involve duality rotations of vectors and thus are not manifest off-shell invariances in standard “second-order” formulation. To study how such symmetries are realised in the quantum theory we consider examples in 2 dimensions where vector-vector duality is replaced by scalar-scalar one. Using “doubled” formulation, where fields and their momenta are treated on an equal footing and the duality becomes a manifest symmetry of the action (at the expense of the Lorentz symmetry), we argue that the corresponding on-shell quantum effective action or S-matrix are duality symmetric as well as Lorentz invariant. The simplest case of discrete Z 2 duality corresponds to a symmetry of the S-matrix under flipping the sign of the negative-chirality scalars in 2 dimensions or phase rotations of chiral (definite-helicity) parts of vectors in 4 dimensions. We also briefly discuss some 4d vector models and comment on implications of our analysis for extended supergravities.

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Authors and Affiliations

  1. Department of Physics, The Pennsylvania State University, University Park, PA, 16802, U.S.A.

    R. Roiban

  2. Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2AZ, U.K.

    A. A. Tseytlin

  3. Lebedev Institute, Moscow, Russia

    A. A. Tseytlin

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  1. R. Roiban
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  2. A. A. Tseytlin
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Correspondence to R. Roiban.

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ArXiv ePrint: 1205.0176

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Roiban, R., Tseytlin, A.A. On duality symmetry in perturbative quantum theory. J. High Energ. Phys. 2012, 99 (2012). https://doi.org/10.1007/JHEP10(2012)099

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