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

TL;DR

Stable gravitational orbits around $AdS$ black holes map to Regge trajectories in the dual CFT, where long-lived bulk states appear as quasi-normal modes on the second sheet and as resonances in the heavy-light OPE. The authors establish a tight link between orbits, QNMs, and infinite towers of double-twist operators, using Bohr-Sommerfeld quantization to compute anomalous dimensions and showing agreement with the light-cone bootstrap in overlapping regimes. They quantify orbit decay via scalar radiation and nonperturbative tunneling, and discuss how perturbative in $1/J$ these states behave as many-body scars, while nonperturbative horizon effects restore a continuum and thermalization. The work unifies bulk and boundary perspectives, highlights a mirage interpretation of discrete double-twist spectra, and maps a path to all-orders predictions and finite-$c_T$ extensions, with implications for holographic bootstrap and quantum scar phenomenology.

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.

Figures (4)

• Figure 1: The exact Regge trajectory for circular orbits versus its large spin expansion approximation. We set $\mu=5$ for which $J_{\rm min} \simeq 196.83 \Delta_L$. For other values of $\mu$ the situation is very similar. (a) We plot the exact Regge trajectory against its large spin approximation given by \ref{['eq:largespin4d']}. The red dashed curve corresponds to only keeping the leading $O(\mu)$ term in \ref{['eq:largespin4d']}. The black dashed curve corresponds to keeping all terms in \ref{['eq:largespin4d']}. The exact Regge trajectory in blue can be plotted using its parameteric representation given by \ref{['eq:orbitsQN']}. (b) The relative error in approximating the exact anomalous dimension $\gamma_{\text{Exact}}$ by its large spin expansion up to order $O(\mu^3)$ as in \ref{['eq:largespin4d']}, which we denote by $\gamma_{\text{LC}}$. We see that the error is of order $10 \%$ at $J= J_{\text{min}}$, and becomes less than $1 \%$ for $J \gtrsim 3 J_{\text{min}}$.
• Figure 2: For $J>J_{\text{min}}(\mu)$, the potential $V(r)$ goes to zero at the horizon $r=r_s$, behaves like $r^2$ for large $r$, and has a metastable minimum at the radial position of the circular orbit. For a given value of $E$, there are three turning points $r_a$, $r_b$, and $r_c$ where $E^2=V(r)$, with $r_a>r_b>r_c$.
• Figure 3: The power spectrum $P_J$ grows like a power law until $J\sim \mu^2$, at which point it begins to decay exponentially.
• Figure 4: We choose a counterclockwise contour that is straight except near the turning points $z_{\pm}$, where the contour is an infinitesimal circular arc. The integral over the straight segments gives the discontinuity across the branch cut, and the divergence at the endpoints is canceled by the circular arcs.