On the explicit asymptotic symmetry breaking of sl(3,R) Jackiw–Teitelboim gravity

Abstract

This study investigates the asymptotic symmetry algebras (ASA) of Jackiw–Teitelboim (JT) gravity within the framework of $\mathfrak{sl}(3,\mathbb{R})$ 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 $\mathfrak{sl}(3,\mathbb{R})$ model, the dilaton field preserves a subset of the complete $W_3$-symmetry, restricting the algebra to $\mathfrak{sl}(3,\mathbb{R})$. 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.