Abstract
We give a prescription for mathcal{N} = 1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition.
Highlights
Where γ is the parameter and (S, P ) are the Lorentz invariants quadratic in the components of the two-form field strength F = dA for a one-form potential A
The Hamiltonian field equations are analytic at the corresponding Hamiltonian field configurations; this is possible because the Legendre transform that takes Lγ to the Hamiltonian density Hγ maps configurations with S = P = 0 to the boundary of the domain in which Hγ is convex [1]
We do this by means of a general prescription that starts with any bosonic nonlinear electrodynamics theory for which the Lagrangian density is a strictly convex function of the electric field; as we show, this condition is required to ensure the absence of superluminal propagation of small-amplitude waves in a constant electromagnetic background
Summary
All nonlinear N = 1 four-dimensional (4D) supersymmetric extensions of Maxwell electrodynamics are based on the same off-shell supermultiplet: the “Maxwell supermultiplet” For this reason it will be useful to begin with a rapid review of the superfield construction of supersymmetric electrodynamics in flat superspace. There are many three-variable bosonic truncations of L(S, P, D) that lead to the same two-variable function L(S, P, 0); this illustrates the well-known fact that two supersymmetric Lagrangians which reduce to the same bosonic one may differ by fermionic terms [28, 29] For this reason we shall focus on a special class of three-variable functions L(S, P, D).
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