Boundary theories for dilaton supergravity in 2D

Abstract

The mathfrak{o}mathfrak{s}mathfrak{p}left(2, mathbb{N}right) -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}ge 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-AdS2 asymptotics.