Supergroup Structure of Jackiw-Teitelboim Supergravity

Abstract

We develop the gauge theory formulation of $\mathcal{N}=1$ Jackiw-Teitelboim supergravity in terms of the underlying $\text{OSp}(1|2,\mathbb{R})$ 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 $\text{OSp}(1|2,\mathbb{R})$ is carried out and interpreted in terms of character insertions in the bulk. From a mathematical perspective, we construct the principal series representations of $\text{OSp}(1|2,\mathbb{R})$ and show that whereas the corresponding Plancherel measure does not match the density of states of $\mathcal{N}=1$ JT supergravity, a restriction to the positive subsemigroup ${\text{OSp}}^{+}(1|2,\mathbb{R})$ 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.

55 pages + extensive appendices, v3: fixed typos and added references, matches published version

References in corpus (21)

• An Investigation of AdS${}_2$ Backreaction and Holography
• Three-Dimensional Gravity Revisited
• Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
• JT gravity as a matrix integral
• Late Time Correlation Functions, Baby Universes, and ETH in JT Gravity
• More quantum noise from wormholes
• Wormholes without averaging
• From operator statistics to wormholes
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Deformations of JT Gravity and Phase Transitions
• Fourier transform and related integral transforms in superspace
• Density matrices in quantum gravity
• N=1 SUSY Conformal Block Recursive Relations
• A JT supergravity as a double-cut matrix model
• Structure constants of the OSP(1|2) WZNW model
• Correlators in higher spin AdS_3 holography from Wilson lines with loop corrections
• On the N=1 super Liouville four-point functions
• Gauge Theory Formulation of Hyperbolic Gravity
• Wormholes in Quantum Mechanics
• 2D holography beyond the Jackiw-Teitelboim model
• The Schwarzian sector of higher spin CFTs

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• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Quantum exponentials for the modular double and applications in gravity models
• Phase transitions for deformations of JT supergravity and matrix models
• Operational islands and black hole dissipation in JT gravity
• Branes in JT (super)gravity from group theory
• On the saturation of late-time growth of complexity in supersymmetric JT gravity
• Gravitational wavefunctions in JT supergravity
• Quantum group origins of edge states in double-scaled SYK
• Holography in CGHS supergravity
• Entanglement entropy in Jackiw-Teitelboim gravity with matter
• Schwarzian for colored Jackiw-Teitelboim gravity
• Boundary Conditions for $\mathrm{Ad}{\mathrm{S}}_2$ Dilaton Gravity
• Fiducial observers and the thermal atmosphere in the black hole quantum throat