### 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.

Original language | English (US) |
---|---|

Article number | 099 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 10 |

DOIs | |

State | Published - Nov 7 2012 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2012*(10), [099]. https://doi.org/10.1007/JHEP10(2012)099

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*Journal of High Energy Physics*, vol. 2012, no. 10, 099. https://doi.org/10.1007/JHEP10(2012)099

**On duality symmetry in perturbative quantum theory.** / Roiban, Radu; Tseytlin, A. A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On duality symmetry in perturbative quantum theory

AU - Roiban, Radu

AU - Tseytlin, A. A.

PY - 2012/11/7

Y1 - 2012/11/7

N2 - 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.

AB - 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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U2 - 10.1007/JHEP10(2012)099

DO - 10.1007/JHEP10(2012)099

M3 - Article

VL - 2012

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 10

M1 - 099

ER -