Generalized symmetries and invariant matter couplings in two-dimensional dilaton gravity

TL;DR

This paper explores the generalized symmetries in two-dimensional dilaton gravity, revealing a continuum of Noether symmetries including area-preserving transformations, and introduces invariant gravity-matter couplings that modify the dilaton potential.

Contribution

It introduces new invariant gravity-matter couplings in 2D dilaton gravity and characterizes the continuum of symmetries, including a half Witt algebra, affecting the dilaton potential and matter interactions.

Findings

Identified a continuum of Noether symmetries including half a Witt algebra.

Constructed metrics invariant under specific symmetries.

Showed invariant couplings reshape the dilaton potential.

Abstract

New features of the generalized symmetries of generic two-dimensional dilaton models of gravity are presented and invariant gravity-matter couplings are introduced. We show that there is a continuum set of Noether symmetries, which contains half a de Witt algebra. Two of these symmetries are area-preserving transformations. We show that gravity-matter couplings which are invariant under area preserving transformations only contribute to the dynamics of the dilaton-gravity sector with a reshaping of the dilaton potential. The interaction with matter by means of invariant metrics is also considered. We show in a constructive way that there are metrics which are invariant under two of the symmetries. The most general metrics and minimal couplings that fulfil this condition are found.