On duality symmetry in perturbative quantum theory

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 a "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 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 models and comment on implications of our analysis for extended supergravities.

21 pages, Latex v2: comments and references added v3: references and minor comments added

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• Democracy from topology
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
• Non-compact duality, super-Weyl invariance and effective actions
• Old Dualities and New Anomalies
• S-dual Amplitude and D3-Brane Couplings
• N=2 Supergravity Counterterms, Off and On Shell
• Self-dual supersymmetric nonlinear sigma models
• Weyl invariance, non-compact duality and conformal higher-derivative sigma models
• Heat kernel approach to the one-loop effective action for nonlinear electrodynamics