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