$\mathcal{N}=1$ Jackiw -Teitelboim supergravity beyond the Schwarzian regime

TL;DR

The paper develops a bulk BF-theoretic formulation of two-dimensional JT gravity and its ${\cal N}=1$ supersymmetric extension based on ${\mathfrak{osp}}(1|2)$, to systematically derive asymptotic symmetry algebras under affine and conformal boundary conditions. By employing coadjoint orbit methods and Drinfeld–Sokolov reduction, it shows that a time-dependent dilaton supermultiplet dynamically breaks the full affine ${\mathfrak{osp}}(1|2)_k$ symmetry to a finite ${\mathfrak{osp}}(1|2)$ subalgebra while simultaneously generating abelian boundary currents, with the conformal sector yielding a classical ${\cal N}=1$ superconformal algebra and central charge $c=3k$. The results generalize previous bosonic analyses (e.g., ${\mathfrak{sl}}(2)$ and ${\mathfrak{sl}}(3)$ cases) to the supersymmetric setting and establish a bulk-based route to boundary dynamics beyond the Schwarzian regime, with potential implications for holographic duals of SYK-like systems and higher-spin AdS$_2$ gravity. The framework provides a structured foundation for exploring quantum extensions, including operator ordering effects and central terms, within a controlled BF-theory and coadjoint-orbit context.

Abstract

We investigate the asymptotic symmetry structure of two--dimensional dilaton gravity in its $\mathcal{N}=1$ supersymmetric extension based on the $\mathfrak{osp}(1|2)$ Lie superalgebra. Within the BF theoretical framework, we analyze affine and superconformal boundary conditions for each case and systematically derive the associated asymptotic symmetry algebras. While the classical theory recovers the Virasoro algebra or its affine enhancement, the supersymmetric extension yields a classical $\mathcal{N}=1$ superconformal algebra, subject to dynamical symmetry breaking mechanisms induced by the dilaton supermultiplet. We find that the boundary behavior of the dilaton not only leads to a reduction of the full affine $\mathfrak{osp}(1|2)_k$ symmetry down to $\tt{O} \tt{S} p(1|2)$, but also introduces an abelian extension through commuting modes. These results reveal a novel interplay between symmetry breaking and symmetry extension in low-dimensional supergravity. Our construction generalizes previous analyses of $sl(2,\mathbb{R})$ dilaton gravity to the supersymmetric domain and offers a consistent foundation for investigating boundary dynamics beyond the Schwarzian regime.