Higher-Spin Gravity in Two Dimensions with Vanishing Cosmological Constant

TL;DR

This paper develops a two-dimensional higher-spin gravity theory with zero cosmological constant using a BF gauge formulation, revealing an infinite spectrum of scalar fields and proposing a method for their backreaction inclusion.

Contribution

It introduces a novel higher-spin gravity model in two dimensions with vanishing cosmological constant based on extended gauge algebras, including an approach for backreaction effects.

Findings

Spectrum contains infinite scalar fields with increasing mass

Framework allows inclusion of backreaction of scalars on gravity

First example of fully interacting higher-spin gravity with zero cosmological constant in 2D

Abstract

In this paper, we use a version of the BF formulation of two-dimensional dilaton gravity that allows to define a gauge theory of the two-dimensional Poincar\'e or Maxwell algebras and several of their higher-spin generalisations, both of finite and infinite dimension. The spectrum of the two-dimensional higher-spin gravity with vanishing cosmological constant based on the extended, infinite-dimensional higher-spin algebra is shown to contain an infinite collection of scalar degrees of freedom with a continuum of ever increasing mass, corresponding to the twisted-(co)adjoint representation. We comment on an approach to include backreaction of the scalar fields on the gravity sector at the level of formal equations of motion, thereby providing a first example of a fully interacting higher-spin gravity theory with vanishing cosmological constant in two dimensions.