On the consistent disformal couplings to fermions

Disformal couplings to fermions lead to a unique derivative coupling to the axial fermionic current, which contains higher derivatives in general. We derive general conditions on consistent disformal couplings by requiring the absence of higher time derivatives, as they typically lead to ghost degrees of freedom. For a two-scalar field disformal transformation, we show that the consistent disformal coupling must have a degenerate field space metric. This allows us to explore consistent, new two-scalar field modified gravity models. We show that the transformation of the Einstein-Hilbert action leads to two-field Horndeski or two-field DHOST theories. Our formalism also applies to disformal transformations with higher derivatives. We derive the consistent subclasses of disformal transformations that include second derivatives of a scalar field and first derivatives of a vector field that lead to generalized U-DHOST and degenerate beyond generalized Proca theories.