Supergroup structure of Jackiw-Teitelboim supergravity

We develop the gauge theory formulation of N = 1 Jackiw-Teitelboim supergravity in terms of the underlying OSp(1 vertical bar 2, R) supergroup, focusing on boundary dynamics and the exact structure of gravitational amplitudes. We prove that the BF description reduces to a super-Schwarzian quantum mechanics on the holographic boundary, where boundary-anchored Wilson lines map to bilocal operators in the super-Schwarzian theory. A classification of defects in terms of monodromies of OSp(1 vertical bar 2, R) is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of OSp(1 vertical bar 2, R) and show that whereas the corresponding Plancherel measure does not match the density of states of N = 1 JT supergravity, a restriction to the positive subsemigroup OSp(+)(1 vertical bar 2, R) yields the correct density of states, mirroring the analogous results for bosonic JT gravity. We illustrate these results with several gravitational applications, in particular computing the late-time complexity growth in JT supergravity.