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State-dressed local operators in the AdS/CFT correspondence

Eyoab Bahiru, Alexandre Belin, Kyriakos Papadodimas, Gabor Sarosi, Niloofar Vardian

TL;DR

Addressing locality in perturbative quantum gravity within AdS/CFT, the paper studies the time-band algebra A of single-trace operators and shows that for states with large energy variance $O(N^2)$ a commutant can emerge in the $1/N$ expansion. It constructs state-dressed bulk observables that commute with the Hamiltonian $H$ to all orders in $1/N$ while reproducing leading HKLL correlators, thereby achieving locality through dressing to state features rather than the boundary. The dressing enables sensible treatment of black hole microstates and supports island-like resolutions by making interior operators effectively commute with boundary dynamics. These results suggest that information can be localized in bulk subregions in perturbative quantum gravity and offer a concrete CFT realization of a state-dependent commutant for the time-band algebra.

Abstract

We examine aspects of locality in perturbative quantum gravity and how information can be localized in subregions. In the framework of AdS/CFT, we consider the algebra of single-trace operators defined in a short time band. We conjecture that, if the state has large energy variance, then this algebra will have a commutant in the 1/N expansion. We provide evidence for this by identifying operators that commute with the conformal field theory Hamiltonian to all orders in 1/N, thus resolving an apparent tension with the gravitational Gauss law. The bulk interpretation is that these operators are gravitationally dressed with respect to features of the state rather than the boundary. We comment on observables in certain black hole microstates and the gravitational dressing in the island proposal.

State-dressed local operators in the AdS/CFT correspondence

TL;DR

Addressing locality in perturbative quantum gravity within AdS/CFT, the paper studies the time-band algebra A of single-trace operators and shows that for states with large energy variance a commutant can emerge in the expansion. It constructs state-dressed bulk observables that commute with the Hamiltonian to all orders in while reproducing leading HKLL correlators, thereby achieving locality through dressing to state features rather than the boundary. The dressing enables sensible treatment of black hole microstates and supports island-like resolutions by making interior operators effectively commute with boundary dynamics. These results suggest that information can be localized in bulk subregions in perturbative quantum gravity and offer a concrete CFT realization of a state-dependent commutant for the time-band algebra.

Abstract

We examine aspects of locality in perturbative quantum gravity and how information can be localized in subregions. In the framework of AdS/CFT, we consider the algebra of single-trace operators defined in a short time band. We conjecture that, if the state has large energy variance, then this algebra will have a commutant in the 1/N expansion. We provide evidence for this by identifying operators that commute with the conformal field theory Hamiltonian to all orders in 1/N, thus resolving an apparent tension with the gravitational Gauss law. The bulk interpretation is that these operators are gravitationally dressed with respect to features of the state rather than the boundary. We comment on observables in certain black hole microstates and the gravitational dressing in the island proposal.
Paper Structure (12 sections, 31 equations, 1 figure)

This paper contains 12 sections, 31 equations, 1 figure.

Table of Contents

  1. I. Introduction
  2. II. Algebras in time bands
  3. III. AdS/CFT setup
  4. IV. Time-shifted states and return amplitude
  5. The return amplitude
  6. V. The operators
  7. A. Vanishing commutator with $H$ to all orders in 1/N
  8. B. Similar action as HKLL operators
  9. C. Interpretation and comments
  10. VI. Black Hole microstates
  11. VII.Discussion
  12. Acknowledgments

Figures (1)

  • Figure 1: A numerical study of the decay of $R_{code}(t)$ as a function of $t$ in the SYK model. The state $\ket{\Psi_{0}}$ is one of the Kourkoulou-Maldacena microstates Kourkoulou:2017zaj. The code subspace is obtained by acting on it with a set of fermionic operators. In the plot $d_{\rm code}=8$. More details will be provided in long.