Invertible disformal transformations with higher derivatives

TL;DR

This paper introduces a higher-derivative generalization of disformal transformations, establishing conditions for invertibility and group structure, and constructs new ghost-free scalar-tensor theories with complex derivative couplings.

Contribution

It systematically develops invertible higher-derivative disformal transformations and derives novel ghost-free scalar-tensor theories with higher-order derivatives.

Findings

Established conditions for invertibility and group structure of generalized disformal transformations.

Constructed a new class of ghost-free scalar-tensor theories with higher derivatives.

Demonstrated the application of transformations to generate theories with complex derivative couplings.

Abstract

We consider a higher-derivative generalization of disformal transformations in $D$-dimensional spacetime and clarify the conditions under which they form a group with respect to the matrix product and the functional composition. These conditions allow us to systematically construct the inverse transformation in a fully covariant manner. Applying the invertible generalized disformal transformation to known ghost-free scalar-tensor theories, we obtain a novel class of ghost-free scalar-tensor theories, whose action contains the third- or higher-order derivatives of the scalar field as well as nontrivial higher-order derivative couplings to the curvature tensor.