2025/09/20 by Gorji, Mohammad Ali, Mukohyama, Shinji, Petrov, Pavel +1 · 1 citation
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2509.16526
In the context of the Higher-Order Maxwell-Einstein-Scalar (HOMES) theories, which are invariant under spacetime diffeomorphisms and U(1) gauge symmetry, we study two broad subclasses: the first is up to linear in Rμναβ, ∇μ∇νϕ, ∇ρFμν and up to quadratic in the vector field strength tensor Fμν; the second is up to linear in ∇μ∇νϕ, contains no second derivatives of vector field and metric, but allows for arbitrary functions/powers of Fμν. Under these assumptions, we systematically derive the most general form of the action that leads to second-order (or lower) equations of motion. We prove that, among 41 possible terms in the first subclass, only four independent higher-derivative terms are allowed: the kinetic gravity braiding term G3(ϕ,X)\Boxϕ in the scalar sector with X = -∇μϕ∇μϕ/ 2; the Horndeski non-minimal coupling term w0(ϕ)RβδαγFαβ Fγδ in the vector field sector, where Fμν is the Hodge dual of Fμν; and two interaction terms between the scalar and vector field sectors: [w1(ϕ,X) gρσ + w2(ϕ,X) ∇ρϕ∇σϕ] ∇β∇αϕ Fαρ Fβσ. For the second subclass, which admits 11 possible terms, three of these four, excluding the Horndeski non-minimal coupling term proportional to w0(ϕ), are allowed. These independent terms serve as the building blocks of each subclass of HOMES. Remarkably, there is no higher-derivative parity-violating term in either subclass. Finally, we propose a new generalization of higher-derivative interaction terms for the case of a charged complex scalar field.