Symmetric Scalars

TL;DR

This paper classifies P(X,φ) scalar field theories with classical symmetries, identifying only three types—DBI, Cuscuton, and Scaling—and explores their implications in various spacetime backgrounds.

Contribution

It provides a complete classification of symmetric P(X,φ) theories and derives constraints on effective field theory coefficients using scaling symmetry.

Findings

Only three symmetric theories: DBI, Cuscuton, Scaling.

Scaling symmetry imposes infinite constraints on Wilsonian coefficients.

Cuscuton and DBI actions have specific symmetry properties in curved spacetimes.

Abstract

We provide a complete classification of Poincar\'e-invariant scalar field theories with an enlarged set of classical symmetries to leading order in derivatives, namely for the so-called $P(X,\phi)$ theories, in two or more spacetime dimensions. We find only three possibilities: Dirac-Born-Infeld, Cuscuton and Scaling theories. The latter two classes of actions involve an arbitrary function of the scalar field. As an application, we use the scaling symmetry to derive an infinite set of constraints on the Wilsonian coefficients of the low-energy Effective Field Theory. Furthermore, we study the extension of these results to cosmological (FLRW) and (Anti-)de Sitter spacetimes. We find in particular that the Cuscuton action has a generic set of symmetries around any background spacetime that possesses Killing vector fields, while the DBI actions have well-known analogues that we summarize explicitly.