Abstract
We generalize the electromagnetic duality between a massless, canonical scalar field and a 2-form gauge field in 4-dimensional spacetime to scalar-tensor theories. We derive the action of 2-form gauge field that is dual to two kinds of scalar-tensor theories: shift symmetric K-essence theory and the shift symmetric Horndeski theory up to quadratic in scalar field. The former case, the dual 2-form has a nonlinear kinetic term. The latter case, the dual 2-form has non-trivial interactions with gravity through Einstein tensor. In both case, the duality relation is modified from usual case, that is, the dual 2-form field is not simply given by the Hodge dual of the gradient of the scalar field.
Highlights
A scalar field interacting with gravity through nontrivial couplings enables us to construct divergent scenarios of both the early- and late-time Universe
At quadratic order in ∇μ∇νφ, where φ is a scalar field and ∇μ is the covariant derivative, the general scalar tensor theory is found in Refs. [8,9,10,11], which is called extended scalar-tensor theory [10] or degenerate higher order derivative scalar tensor (DHOST) theory [11]
Let us begin with reviewing the well-known duality between a massless scalar field with the Chern-Simons coupling and a two-form field [18,19,20]
Summary
A scalar field interacting with gravity through nontrivial couplings enables us to construct divergent scenarios of both the early- and late-time Universe. General theory with second-order Euler-Lagrange equations called vector-Horndeski theory [13]. If one relaxes Uð1Þ gauge symmetry and considers a massive vector field, a study of nontrivial interactions with gravity has been developed by an analogy of the Horndeski theory for a scalar field. This is called generalized Proca theory [14]. We review the derivation of the electromagnetic duality between a canonical scalar field and a two-form field including the Chern-Simons coupling.
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