Unruh detectors and quantum chaos in JT gravity

We identify the spectral properties of Hawking-Unruh radiation in the eternal black hole at ultra low energies as a probe for the chaotic level statistics of quantum black holes. Level repulsion implies that there are barely Hawking particles with an energy smaller than the level separation. This effect is experimentally accessible by probing the Unruh heat bath with a linear detector. We provide evidence for this effect via explicit and exact calculations in JT gravity building on a radar definition of bulk observables in the model. Similar results are observed for the bath energy density. This universal feature of eternal Hawking radiation should resonate into the evaporating setup.Comment: 41 pages, v2: added references, fixed some typo

Clocks and Rods in Jackiw-Teitelboim Quantum Gravity

We specify bulk coordinates in Jackiw-Teitelboim (JT) gravity using a boundary-intrinsic radar definition. This allows us to study and calculate exactly diff-invariant bulk correlation functions of matter-coupled JT gravity, which are found to satisfy microcausality. We observe that quantum gravity effects dominate near-horizon matter correlation functions. This shows that quantum matter in classical curved spacetime is not a sensible model for near-horizon matter-coupled JT gravity. This is how JT gravity, given our choice of bulk frame, evades an information paradox. This echoes into the quantum expectation value of the near-horizon metric, whose analysis is extended from the disk model to the recently proposed topological completion of JT gravity. Due to quantum effects, at distances of order the Planck length to the horizon, a dramatic breakdown of Rindler geometry is observed.Comment: 37 pages + appendices, v4: improved discussion on conformal anomaly and choice of bulk observable, added appendix on massive bulk correlators and global conformal blocks, corrected several equations in section 5 and appendix E, typos corrected, matches published versio

Edge Dynamics from the Path Integral: Maxwell and Yang-Mills

We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the edge action in several applications. For Maxwell in Rindler space, we recover earlier results, now embedded in a dynamical canonical framework. A second application is 2d Yang-Mills theory where the boundary action becomes just the particle-on-a-group action. Correlators of boundary-anchored Wilson lines in 2d Yang-Mills are matched with, and identified as correlators of bilocal operators in the particle-on-a-group edge model.Comment: 50 pages, v2: typos corrected and references added, matches published versio

The Schwarzian Theory - A Wilson Line Perspective

We provide a holographic perspective on correlation functions in Schwarzian quantum mechanics, as boundary-anchored Wilson line correlators in Jackiw-Teitelboim gravity. We first study compact groups and identify the diagrammatic representation of bilocal correlators of the particle-on-a-group model as Wilson line correlators in its 2d holographic BF description. We generalize to the Hamiltonian reduction of SL(2,R) and derive the Schwarzian correlation functions. Out-of-time ordered correlators are determined by crossing Wilson lines, giving a 6j-symbol, in agreement with 2d CFT results.Comment: 28 pages + appendices, v3: corrected discussion on representation theory and improved discussion on higher-point functions in appendices, references added, typos corrected, matches published versio

Edge State Quantization: Vector Fields in Rindler

We present a detailed discussion of the entanglement structure of vector fields through canonical quantization. We quantize Maxwell theory in Rindler space in Lorenz gauge, discuss the Hilbert space structure and analyze the Unruh effect. As a warm-up, in 1+1 dimensions, we compute the spectrum and prove that the theory is thermodynamically trivial. In d+1 dimensions, we identify the edge sector as eigenstates of horizon electric flux or equivalently as states representing large gauge transformations, localized on the horizon. The edge Hilbert space is generated by inserting a generic combination of Wilson line punctures in the edge vacuum, and the edge states are identified as Maxwell microstates of the black hole. This construction is repeated for Proca theory. Extensions to tensor field theories, and the link with Chern-Simons are discussed.Comment: 57 pages, v2: minor modifications and references added, matches published versio

Fine Structure of Jackiw-Teitelboim Quantum Gravity

We investigate structural aspects of JT gravity through its BF description. In particular, we provide evidence that JT gravity should be thought of as (a coset of) the noncompact subsemigroup SL$^+$(2,R) BF theory. We highlight physical implications, including the famous sinh Plancherel measure. Exploiting this perspective, we investigate JT gravity on more generic manifolds with emphasis on the edge degrees of freedom on entangling surfaces and factorization. It is found that the one-sided JT gravity degrees of freedom are described not just by a Schwarzian on the asymptotic boundary, but also include frozen SL$^+$(2,R) degrees of freedom on the horizon, identifiable as JT gravity black hole states. Configurations with two asymptotic boundaries are linked to 2d Liouville CFT on the torus surface.Comment: 37 pages + appendices, v3: added extensive discussion on the gluing measure (comparing with the recent work of Saad-Shenker-Stanford), clarified discussion on factorization and explicit volume factors, and added evidence from hyperbolic geometry, added references, matches published versio

Eigenbranes in Jackiw-Teitelboim gravity

It was proven recently that JT gravity can be defined as an ensemble of L x L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with 1<<N<<L eigenvalues held fixed. This corresponds to a version of JT gravity which includes N FZZT type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.Comment: 25 pages + appendices; v2: matches published versio

65 Cybele in the thermal infrared: Multiple observations and thermophysical analysis

We investigated the physical and thermal properties of 65 Cybele}, one of the largest main-belt asteroids. Based on published and recently obtained thermal infrared observations, including ISO measurements, we derived through thermophysical modelling (TPM) a size of 302x290x232 km (+/- 4 %) and an geometric visible albedo of 0.050+/-0.005. Our model of a regolith covered surface with low thermal inertia and "default" roughness describes the wavelengths and phase angle dependent thermal aspects very well. Before/after opposition effect and beaming behaviour can be explained in that way. We found a constant emissivity of 0.9 at wavelengths up to about 100 micron and lower values towards the submillimetre range, indicating a grain size distribution dominated by 200 micron particle sizes. The spectroscopic analysis revealed an emissivity increase between 8.0 and 9.5 micron. We compared this emissivity behaviour with the Christiansen features of carbonaceous chondrite meteorites, but a conclusive identification was not possible. A comparison between the Standard Thermal Model (STM) and the applied TPM clearly demonstrates the limitations and problems of the STM for the analysis of multi-epoch and -wavelengths observations. While the TPM produced a unique diameter/albedo solution, the calculated STM values varied by +/-30 % and showed clear trends with wavelength and phase angle. Cybele can be considered as a nice textbook case for the thermophysical analysis of combined optical and thermal infrared observations.Comment: 11 pages, 8 figures, accepted for publication by A&