ASC Workshops

In this talk we calculate the entanglement entropy in the presence of a moving mirror in a CFT. We employ the AdS/BCFT construction to describe a gravity dual of moving mirrors. We will show that the time evolution of entanglement entropy for a class of moving mirror, which models an evaporating black hole, follows an ideal page curve. In this gravity dual of this model and also in earlier works on holographic page curves, the end of the world-brane in AdS plays a crucial role. I will also present our recent result on their chaotic spectrum in holographic CFTs.

In this talk I will discuss circuit complexity in the setting of higher dimensional conformal field theories. I will consider unitary gates built from a representation of the conformal group, two different circuit cost functions defined using either the Fubini-Study metric or the one-norm, and paths that start from an initial spinless primary state. We will see that the resulting Fubini-Study metric is the metric on a particular coadjoint orbit of the conformal group, while the one-norm computes the geometric action associated to this orbit. This generalizes recent results in 2d connecting the one-norm to a Virasoro geometric action, and also shows that coadjoint orbits provide a unified geometric framework that applies to different choices of cost functions. I will end with some comments about symmetry groups other than the conformal group, using group theoretic generalizations of coherent states. This is based on a work with Nicolas Chagnet, Jan de Boer and Claire Zukowski.

Computational complexity is a quantum information concept that recently has found applications in holography. I will consider quantum computational complexity for n qubits using Nielsen's geometrical approach. In the definition of complexity there is a big amount of arbitrariness due to the choice of the penalty factors, which parameterize the cost of the elementary computational gates. In order to reproduce desired features in holography, negative sectional curvatures are required. With the simplest choice of penalties, this is achieved at the price of singular curvatures in the large n limit. I will consider a choice of penalties in which negative curvatures can be obtained in a smooth way. I will also talk about the relation between operator and state complexities, framing the discussion in the language of Riemannian submersions. Finally, I'll discuss conjugate points for a large number of qubits in the unitary space and I'll provide a strong indication that maximal complexity scales exponentially with the number of qubits in a certain regime of the penalties space.

I will present the connection between the Wheeler-DeWitt approach for two-dimensional quantum gravity and holography, focusing in the case of Liouville theory coupled to c = 1 matter. The analysis is in a spirit similar to the recent studies of Jackiw-Teitelboim gravity. Matrix quantum mechanics and the associated double scaled fermionic field theory, are providing the complete dynamics of such two-dimensional universes with c=1 matter, including the effects of topology change.

The pole skipping phenomenon is a subtle effect in the thermal energy density retarded two point function at a special point in the complex frequency and momentum planes. For maximally chaotic theories, this special point is related to data characterising the butterfly effect, and is explained by a common dynamical origin of energy transport and scrambling. I will argue that pole skipping also happens in non-maximally chaotic theories and its location corresponds to the stress tensor contribution to many body chaos. I will test this proposal in the large q limit of an SYK chain, where I determine both the Lyapunov growth of the OTO correlator and the energy density two point function exactly as a function of the coupling, interpolating between weekly coupled and maximally chaotic behaviour.

A salient feature of black holes near extremality is the appearance of an AdS2 throat in their near-horizon geometry. Depending on the underlying theory, these AdS2 throats may be unstable to fragmentation, wherein a single throat is instead replaced by a tree-like structure of branched AdS2 throats. For Einstein-Maxwell theory, the underlying reason behind this instability is the existence of multi-centered configuration in the moduli space of black hole solutions at fixed total charge. Given the success of the Schwarzian/SYK paradigm for understanding a single AdS2 it is time to revisit the fragmentation story. To build up intuition, I will present a model, studied in the statistical mechanics literature, that shares many features with SYK, including exact solvability at large-N and an emergent conformal symmetry that gets weakly broken in the UV. The novel feature of this model is the appearance of a spin glass phase at O(1) temperatures, which I will try to relate to the fragmentation story.

Domain walls between Anti-de Sitter vacua are important for the study of the string-theory landscape, and enter in recent toy models of black hole evaporation. In this talk I will describe the phase diagram of a simple 2+1 dimensional model of thin domain walls anchored at the AdS boundary, and I will comment on its dual holographic interpretation.

Euclidean wormholes comprise exotic types of gravitational solutions, that still challenge our physical intuition and understanding. In the first part of the talk, I will analyse asymptotically AdS wormhole solutions in the context of holography. From a bottom up perspective a study of correlation functions of local and non-local operators indicates the universal properties that any putative holographic dual should exhibit. The system is very weakly cross-coupled in the UV, and becomes strongly cross-coupled in the IR. In the second part, I will describe some concrete field theoretic setups which exhibit such a behaviour and comment on various issues arising in the alpha-parameter interpretation of the wormhole gas.

We consider the effect of shockwaves on the entanglement structure of black holes. We examine the correlations in generic subsets of the Hawking radiation emitted by evaporating black holes following the shockwave insertion and find a zoo of competing island saddle points for the associated entanglement entropies. By computing the mutual information between early and late modes we establish long range correlations in the Hawking radiation.

Quantum Complexity, Integrability, and Chaos

The states of quantum systems grow in complexity over time as entanglement spreads between degrees of freedom. Following ideas in computer science, we formulate the complexity of evolution as the length of the shortest geodesic on the unitary group manifold between the identity and the time evolution operator, and use the SYK family of models with N fermions to study this quantity in free, integrable, and chaotic systems. In all cases, the complexity initially grows linearly in time, and the shortest path lies along the physical time evolution. This linear growth is eventually truncated by "shortcuts" on the unitary manifold that are shorter than the physical time evolution. We explicitly locate such shortcuts and hence show that in the free theory, shortcuts occur at a time of O(N^1/2), truncating complexity growth at this scale. We also find an explicit operator which "fast-forwards" time evolution with this complexity. In a class of integrable theories, we show that shortcuts appear in a time upper bounded by O(poly(N)), again truncating complexity growth. Finally, in chaotic theories we argue that shortcuts do not occur until exponential times, after which it becomes possible to find infinitesimally nearby fixed-complexity approximations to the time evolution operator. We relate these results to the Eigenstate Complexity Hypothesis, a new criterion on the spectrum of energy eigenstates that guarantees an exponential increase of complexity over time that is consistent with maximal chaos.