### 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) |
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Article number | 99 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 10 |

DOIs | |

State | Published - Jan 1 2012 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

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## Cite this

*Journal of High Energy Physics*,

*2012*(10), [99]. https://doi.org/10.1007/JHEP10(2012)099