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

Abstract This study investigates the asymptotic symmetry algebras (ASA) of Jackiw–Teitelboim (JT) gravity within the framework of $$\mathfrak {sl}(3,\mathbb {R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>sl</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> 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 $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> boundary. For the $$\mathfrak {sl}(3,\mathbb {R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>sl</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> model, the dilaton field preserves a subset of the complete $$W_3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> -symmetry, restricting the algebra to $$\mathfrak {sl}(3,\mathbb {R})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>sl</mml:mi> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . These results provide deeper insights into the role of dilaton dynamics in holographic dualities, with implications for the thermodynamics and geometry of AdS $$_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>2</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> . The findings pave the way for systematically exploring extended gauge symmetries in two-dimensional gravity and their relevance to higher-rank Lie algebras.