ABSTRACT
We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the SO(2) duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to p-forms in 2p+2 dimensions.
ABSTRACT
We analyze the constraints imposed by gauge invariance on higher-order interactions between massless bosonic fields in three-dimensional higher-spin gravities. Focusing on the transverse-traceless part, we show that vertices of quartic and higher order that are independent of the cubic ones can only involve scalars and Maxwell fields. As a consequence, the full nonlinear interactions of massless higher-spin fields are completely fixed by the cubic vertex.
ABSTRACT
In this Letter, we take the first step towards construction of nontrivial Lagrangian theories of higher-spin gravity in a metriclike formulation in three dimensions. The crucial feature of a metriclike formulation is that it is known how to incorporate matter interactions into the description. We derive a complete classification of cubic interactions for arbitrary triples s_{1}, s_{2}, s_{3} of massless fields, which are the building blocks of any interacting theory with massless higher spins. We find that there is, at most, one vertex for any given triple of spins in 3D (with one exception, s_{1}=s_{2}=s_{3}=1, which allows for two vertices). Remarkably, there are no vertices for spin values that do not respect strict triangle inequalities and contain at least two spins greater than one. This translates into selection rules for three-point functions of higher-spin conserved currents in two dimensional conformal field theory. Furthermore, universal coupling to gravity for any spin is derived. Last, we argue that this classification persists in arbitrary Einstein backgrounds.
