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

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.