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

TL;DR

This paper explores the asymptotic symmetries of two-dimensional $ ext{N}=1$ supergravity, revealing how boundary conditions induce a reduction from affine superalgebra to a superconformal algebra, extending previous non-supersymmetric analyses.

Contribution

It generalizes the analysis of boundary symmetries in dilaton gravity to include supersymmetry, establishing a framework beyond the Schwarzian regime.

Findings

Derivation of the $ ext{N}=1$ superconformal algebra as the asymptotic symmetry.

Identification of the dynamical reduction of affine $ ext{osp}(1|2)$ symmetry.

Demonstration of boundary behavior inducing symmetry breaking and extension.

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 and systematically derive the corresponding asymptotic symmetry algebra(ASA). While the bosonic theory reproduces the Virasoro algebra and its affine enhancement, the supersymmetric extension yields a classical $\mathcal{N}=1$ superconformal algebra whose realization is dynamically restricted by the dilaton supermultiplet. We show that the boundary behavior of the dilaton induces a controlled dynamical reduction of the full affine $\mathfrak{osp}(1|2)_k$ symmetry to its $\tt{O}\tt{S}p(1|2)$ stabilizer subalgebra, while simultaneously generating an abelian ideal composed of mutually commuting modes. This establishes a coherent interplay between asymptotic symmetry breaking and symmetry extension in low--dimensional supergravity.Our construction generalizes previous analyses of $\mathfrak{sl}(2,\mathbb{R})$ dilaton gravity to the supersymmetric setting and provides a consistent bulk--based framework for investigating boundary dynamics beyond the Schwarzian regime.