Boundary theories for dilaton supergravity in 2D

TL;DR

This paper develops a BF formulation of dilaton supergravity in two dimensions with gauge group $OSp(2,N)$ and analyzes boundary dynamics under carefully chosen asymptotic conditions. By foliating the phase space into super-Virasoro coadjoint orbits and imposing integrability and regularity (holonomy) requirements, the authors derive reduced boundary theories that are either extended super-Schwarzian models or (super)particle mechanics, depending on the Casimir. The analysis is first carried out for $N=1$, then extended to $N=2$ using the loop group of $OSp(2,2)$, and finally generalized to $N>2$ via appropriate boundary conditions; in all cases the on-shell bulk action reduces to a boundary action capturing the essential dynamics. The results illuminate how boundary degrees of freedom encode holographic information in supersymmetric 2D gravity and suggest pathways to link with supersymmetric SYK-like models and quantum boundary observables, with potential extensions to AdS$_2$/superconformal holography and entanglement structure.

Abstract

The $\mathfrak{osp}(2,N)$-BF formulation of dilaton supergravity in two dimensions is considered. We introduce a consistent class of asymptotic conditions preserved by the extended superreparametrization group of the thermal circle at infinity. In the $N=1$ and $N=2$ cases the phase space foliation in terms of orbits of the super-Virasoro group allows to formulate suitable integrability conditions for the boundary terms that render the variational principle well-defined. Once regularity conditions are imposed, requiring trivial holonomy around the contractible cycle the asymptotic symmetries are broken to some subsets of exact isometries. Different coadjoint orbits of the asymptotic symmetry group yield different types of boundary dynamics; we find that the action principle can be reduced to either the extended super-Schwarzian theory, consistent with the dynamics of a non-vanishing Casimir function, or to superparticle models, compatible with bulk configurations whose Casimir is zero. These results are generalized to $\mathcal{N} \geq 3$ by making use of boundary conditions consistent with the loop group of OSp$(2,N)$. Appropriate integrability conditions permit to reduce the dynamics of dilaton supergravity to a particle moving on the OSp$(2,N)$ group manifold. Generalizations of the boundary dynamics for $\mathcal{N}>2$ are obtained once bulk geometries are supplemented with super-AdS$_2$ asymptotics.