Gravitational orbits, double-twist mirage, and many-body scars

TL;DR

This paper investigates the relationship between gravitational orbits around AdS black holes, boundary conformal field theory resonances, and the emergence of many-body scars, providing new insights into their connections and decay mechanisms.

Contribution

It establishes a detailed connection between gravitational orbits, quasi-normal modes, and double-twist operators, and explores the nature of many-body scars in holographic theories.

Findings

Computed anomalous dimensions of double-twist operators using corrected Bohr-Sommerfeld formula.

Found perfect agreement between quasi-normal mode predictions and light-cone bootstrap results.

Analyzed decay times and tunneling rates of gravitational orbits.

Abstract

We explore the implications of stable gravitational orbits around an AdS black hole for the boundary conformal field theory. The orbits are long-lived states that eventually decay due to gravitational radiation and tunneling. They appear as narrow resonances in the heavy-light OPE when the spectrum becomes effectively continuous due to the presence of the black hole horizon. Alternatively, they can be identified with quasi-normal modes with small imaginary part in the thermal two-point function. The two pictures are related via the eigenstate thermalisation hypothesis. When the decay effects can be neglected the orbits appear as a discrete family of double-twist operators. We investigate the connection between orbits, quasi-normal modes, and double-twist operators in detail. Using the corrected Bohr-Sommerfeld formula for quasi-normal modes, we compute the anomalous dimension of double-twist operators. We compare our results to the prediction of the light-cone bootstrap, finding perfect agreement where the results overlap. We also compute the orbit decay time due to scalar radiation and compare it to the tunneling rate. Perturbatively in spin, in the light-cone bootstrap framework double-twist operators appear as a small fraction of the Hilbert space which violate the eigenstate thermalization hypothesis, a phenomenon known as many-body scars. Nonperturbatively in spin, the double-twist operators become long-lived states that eventually thermalize. We briefly discuss the connection between perturbative scars in holographic theories and known examples of scars in the condensed matter literature.