On the Explicit Asymptotic Symmetry Breaking of sl(3,R) Jackiw-Teitelboim Gravity

TL;DR

This work analyzes the asymptotic symmetry algebra (ASA) of Jackiw–Teitelboim gravity extended to $\mathfrak{sl}(3,\mathbb{R})$ via a BF-theoretic formulation. By deriving both affine and conformal boundary conditions, the authors show how a time-dependent dilaton dynamically breaks the complete $\mathcal{W}_3$ symmetry, reducing the ASA to a finite-dimensional $\mathfrak{sl}(3,\mathbb{R})$ subalgebra while simultaneously generating abelian currents that extend the boundary dynamics. Under conformal boundary conditions, the classical $\mathcal{W}_3$ structure emerges with central charge $c=3k$, but dilaton fluctuations deform this algebra, indicating a multi-component boundary action beyond the Schwarzian. The results illuminate how higher-spin gauge symmetries and dilaton dynamics shape holographic duals in AdS$_2$, offering a systematic framework for exploring higher-rank extensions and potential connections to SYK-like models. Overall, the BF formalism provides a coherent route to understanding symmetry breaking and extension at the boundary of two-dimensional gravity with higher-spin fields.

Abstract

This study investigates the asymptotic symmetry algebras (ASA) of Jackiw-Teitelboim (JT) gravity within the framework of sl(3,R) symmetry. By explicitly constructing this algebra, we explore how the presence of the dilaton field influences the structure of asymptotic symmetries and symmetry breaking mechanisms at the AdS(2) boundary. For the sl(3,R) model, the dilaton field preserves a subset of the complete W(3)-symmetry, restricting the algebra to sl(3,R). These results provide deeper insights into the role of dilaton dynamics in holographic dualities, with implications for the thermodynamics and geometry of AdS(2). The findings pave the way for systematically exploring extended gauge symmetries in two-dimensional gravity and their relevance to higher-rank Lie algebras.