On the Conformal Symmetry of Exceptional Scalar Theories

TL;DR

This paper uncovers the conformal symmetry structure of exceptional scalar theories like DBI and special galileon, revealing their algebraic properties and invariance under Weyl transformations, even at unphysical dimensions.

Contribution

It explicitly derives the Lagrangian form of conformal symmetry for these theories and identifies the larger algebraic structures they form, extending understanding of their symmetry properties.

Findings

Conformal symmetry is non-linearly realized in these theories.

New symmetries form a larger algebra, related to higher-dimensional conformal algebra.

Theories can be made Weyl invariant with appropriate improvement terms.

Abstract

The DBI and special galileon theories exhibit a conformal symmetry at unphysical values of the spacetime dimension. We find the Lagrangian form of this symmetry. The special conformal transformations are non-linearly realized on the fields, even though conformal symmetry is unbroken. Commuting the conformal transformations with the extended shift symmetries, we find new symmetries, which when taken together with the conformal and shift symmetries close into a larger algebra. For DBI this larger algebra is the conformal algebra of the higher dimensional bulk in the brane embedding view of DBI. For the special galileon it is a real form of the special linear algebra. We also find the Weyl transformations corresponding to the conformal symmetries, as well as the necessary improvement terms to make the theories Weyl invariant, to second order in the coupling in the DBI case and to lowest order in the coupling in the special galileon case.