In this paper, we study excited states in anti–de Sitter (AdS) space prepared by local operator insertions of a massive scalar field, corresponding to local operator quenches in a free bulk scalar theory. Using the AdS/CFT correspondence, we compute the time evolution of boundary observables in the dual conformal field theory states. We then introduce a hard wall in AdS Poincare coordinates to impose an infrared cutoff (“hard wall”), thereby creating a confining deformation of the dual conformal field theory, and analyze the dynamics of excited states in this confining background. By comparing the evolution of boundary two-point correlation functions in the deformed theory with the statistics of Gaussian random matrix ensembles, we show that for sufficiently heavy operators, the spacing-ratio statistics of peaks in the temporal dynamics are closest to those of the Gaussian symplectic ensemble. Finally, we extend the analysis to the compact Bañados-Teitelboim-Zanelli black hole and to its hard-wall deformation, where we find qualitatively similar trends.
In this paper, we study excited states in anti–de Sitter (AdS) space prepared by local operator insertions of a massive scalar field, corresponding to local operator quenches in a free bulk scalar theory. Using the AdS/CFT correspondence, we compute the time evolution of boundary observables in the dual conformal field theory states. We then introduce a hard wall in AdS Poincare coordinates to impose an infrared cutoff (“hard wall”), thereby creating a confining deformation of the dual conformal field theory, and analyze the dynamics of excited states in this confining background. By comparing the evolution of boundary two-point correlation functions in the deformed theory with the statistics of Gaussian random matrix ensembles, we show that for sufficiently heavy operators, the spacing-ratio statistics of peaks in the temporal dynamics are closest to those of the Gaussian symplectic ensemble. Finally, we extend the analysis to the compact Bañados-Teitelboim-Zanelli black hole and to its hard-wall deformation, where we find qualitatively similar trends.
The AdS/CFT correspondence conjectures a duality between quantum gravity theories in anti-de Sitter (AdS) spacetime and conformal field theories (CFTs) on the boundary. One intriguing aspect of this correspondence is that it offers a pathway to explore quantum gravity through tabletop experiments. Recently, a multi-scale entanglement renormalization ansatz (MERA) model of AdS/CFT that can be implemented using contemporary quantum simulators has been proposed [R. Sahay, M. D. Lukin, and J. Cotler, arXiv:2401.13595 (2024)]. Particularly, local bulk excitations (entitled "hologrons") manifesting attractive interactions given by AdS gravity were found. However, the fundamental question concerning the stability of these identified hologrons is still left open. Here, we address this question and find that hologrons are unstable during dynamic evolution. In searching for stable bulk excitations with attractive interactions, we find they can be constructed by the local primary operators in the boundary CFT. Furthermore, we identify a class of boundary excitations that exhibit the bizarre behavior of "holographic transportation", which can be directly observed on the boundary system implemented in experiments.
Fast scrambling and exponential growth of complexity are two distinctive features of quantum gravity, offering a unique window into the mechanisms that govern the semiclassical limit of the holographic duality. In this thesis, we explore these information-theoretic phenomena through two key diagnostics --- out-of-time ordered correlation functions (OTOCs) and spread complexity --- computed in the setting of two-dimensional holographic conformal field theories (CFTs). First, we focus on the large-c limit of Liouville theory, where the computation of OTOCs reveals distinctive insights into both the chaotic nature and the structural features of the theory. Remarkably, we find it exhibits a maximal Lyapunov exponent, despite lacking the identity operator in its spectrum, and a scrambling time logarithmic in the central charge. Using path integral techniques, we calculate heavy-light four-point functions, and uncover a conformal block expansion dominated by the exchange of an infinite tower of spinless double-trace operators. We attribute the chaotic behaviour of the OTOC to this exchange of operators, which can be thought of as dressed scramblons. Additionally, we observe that at the onset of scrambling, the dominance of conformal blocks shifts from heavy primaries at early times to light primaries at late times. Second, we turn to the diagnostic of spread complexity in locally excited holographic CFTs and argue that its time derivative is dual to the proper radial momentum of a massive point particle propagating in Anti-de Sitter spacetime (AdS). Exploiting the conformal symmetry and the emergence of an ``effective'' SL(2,R) group, we employ representation-theoretic techniques to compute return amplitudes, Lanczos coefficients, and spread complexities. We then verify our conjectured duality for three settings: the CFT on the line, dual to Poincaré AdS; the CFT on the circle, dual to global AdS; and the CFT at finite temperature, dual to a BTZ black hole. In the gravitational theory, the same SL(2,R) structure emerges as the isometry group of the infalling plane of the bulk particle. Third, we generalise the analysis of spread complexity to modular Hamiltonian evolution. Exploiting the rich algebraic structure of modular theory, we construct the modular Hamiltonians Kₘ and the half-sided modular translations G for the three example states above. Leveraging conformal symmetry, we once again compute modular return amplitudes, Lanczos coefficients, and modular spread complexities. In particular, we emphasise the role of ``conformal regularisation'' --- i.e. regulating with the operator that generates modular evolution - in preserving the effective SL(2,R) structure of the amplitudes. We find that evolution under Kₘ exhibits thermal spread complexity for β = 1 across all examples, while G-evolution universally leads to quadratic growth. Finally, we provide a formal explanation of these results, identifying the role of the Killing norm D of the evolution operator as the key factor governing the behaviour of complexity.
We study interacting scalar quantum field theories in anti-de Sitter (AdS) space using a tensor-network approach based on matrix product states. We develop methods for extracting low-lying boundary spectra from global-AdS energy levels, probing bulk criticality through finite-size scaling in the AdS radius, and identifying conformal boundary conditions. Applying these methods to scalar ϕ4 theory in AdS2, we compute the lowest non-trivial Z2-odd and even boundary scaling dimensions non-perturbatively. We then locate the bulk Z2 symmetry-breaking transition and extract critical exponents and central charge consistent with the 2D Ising universality class. At the critical point, we determine the low-lying boundary spectrum and use it to identify the Z2-preserving free/ordinary Ising conformal boundary condition, thereby characterising both the bulk and boundary universality classes.
A bstract Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume of constant timeslices of AdS leads to divergences in the energy levels. We propose a simple prescription to obtain finite physical energies and test it with numerical diagonalization in several models: the free massive scalar field, ϕ 4 theory, Lee-Yang and Ising field theory. Along the way, we discuss spontaneous symmetry breaking in AdS and derive a compact formula for perturbation theory in quantum mechanics at arbitrary order. Our results suggest that all conformal boundary conditions for a given theory are connected via bulk renormalization group flows in AdS.
The surface/state correspondence suggests that the bulk codimensional two surface could be dual to the quantum state in the holographic conformal field theory (CFT). Inspired by the cutoff-anti--de Sitter (AdS)/TT-deformed-CFT correspondence, we propose that the quantum states of the two-dimensional TT-deformed holographic CFT are dual to some particular surfaces in the AdS3 gravity. In particular, the time slice of the cutoff surface is dual to the ground state of the TT-deformed CFT. We examine our proposal by studying the entanglement entropy and complexity. We find that the complexity of the ground state in the deformed theory is consistent with the one of a particular cMERA and the holographic complexity via CV or CA prescription.
Abstract Quantum corrections to the entanglement entropy of matter fields interacting with dynamical gravity have proven to be very important in the study of the black hole information problem. We consider a one-particle excited state of a massive scalar field infalling in a pure AdS3 geometry and compute these corrections for bulk subregions anchored on the AdS boundary. In the dual CFT2, the state is given by the insertion of a local primary operator and its evolution thereafter. We calculate the area and bulk entanglement entropy corrections at order O(N0), O N 0 , both in AdS and its CFT dual. The two calculations match, thus providing a non-trivial check of the FLM formula in a dynamical setting. Further, we observe that the bulk entanglement entropy follows a Page curve. We explain the precise sense in which our setup can be interpreted as a simple model of black hole evaporation and comment on the implications for the information problem.