Abstract
Understanding the consequences of the ${E}_{7(7)}$ duality on the UV properties of $\mathcal{N}=8$ supergravity requires unravelling when and how duality-covariant actions can be constructed so as to accommodate duality-invariant counterterms. For nonsupersymmetric Abelian gauge theories exhibiting $U(1)$-duality, with and without derivative couplings, it was shown that such a covariant construction is always possible. In this paper we describe a similar procedure for the construction of covariant nonlinear deformations of $U(1)$-duality invariant theories in the presence of rigid $\mathcal{N}=2$ supersymmetry. This is a concrete step towards studying the interplay of duality and extended supersymmetry.
Highlights
When the equations of motion of a classical field theory are said to respect a duality invariance, they are invariant under the rotation of an electric field into its magnetic field or of a field strength into its dual field strength
The conservation of the NGZ current leads to non-trivial constraints on the possible deformations of the theories, as the addition of duality-invariant terms does not generically preserve the duality invariance of the equations of motion
An essential ingredient in these constraints is the fact that the dual field strengths are determined by the equations of motion which receive contributions from the deformation terms and modify the NGZ current
Summary
When the equations of motion of a classical field theory are said to respect a duality invariance, they are invariant under the rotation of an electric field into its magnetic field or of a field strength into its dual field strength. The procedures outlined in [11] involved adding one nonlinear initial deformation source to the consistency relations imposed by the tree-level duality transformations and solving them – resulting in an infinite number of terms contributing to the effective action Such consequences are in line with expectations based on soft scalar limits [5] in the case of N = 8 supergravity. A necessary step for the extension of this procedure to supergravity theories (and for showing that it is possible to preserve the classical duality symmetry in the presence of quantum corrections) is the construction of supersymmetric theories of vector multiplets exhibiting duality symmetries Such actions have been constructed previously through different methods: a manifestly supersymmetric Born-Infeld model was constructed in [14], nonlinear superfield actions with spontaneously broken supersymmetry were studied in [15,16,17], and models with manifest supersymmetry and non-linear electromagnetic duality were developed in [18,19,20,21].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
