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We study Generalized Free Fields (GFF) from the point of view of information measures. We begin by reviewing conformal GFF, their holographic representation, and the multiple possible assignations of algebras to a single spacetime region that arise in these theories. We will focus on manifestations of these features present in the Mutual Information (MI) of holographic GFF. First, we show that the MI can be expected to be finite even if the AdS dual space is of infinite volume. Then, we present the long-distance limit of the MI for regions with arbitrary boundaries in the light cone for the causal and entanglement wedge algebras. The pinching limit of these surfaces shows the GFF behaves as an interacting model from the MI point of view. The entanglement wedge algebra choice allows these models to ``fake'' causality, giving results consistent with their role in the description of large N models. Finally, we explore the short distance limit of the MI. Interestingly, we find that the GFF has a leading volume term rather than an area term and a logarithmic term in any dimension rather than only for even dimensions as in ordinary CFTs. We also find the dependence of some subleading terms on the conformal dimension of the GFF.

In this talk, we will first present an analysis of infinitesimal null deformations for the entanglement entropy, which leads to a major simplification of the proof of the C, F and A-theorems in quantum field theory. Next, we will discuss the quantum null energy condition (QNEC) on the light-cone. Finally, we combine these tools in order to establish the irreversibility of renormalization group flows on planar d-dimensional defects, embedded in D-dimensional conformal field theories. This proof completes and unifies all known defect irreversibility theorems for defect dimensions below d=5. The F-theorem on defects (d=3) is a new result using information-theoretic methods. The geometric construction connects the proof of irreversibility with and without defects through the QNEC inequality in the bulk, and makes contact with the proof of strong subadditivity of holographic entropy taking into account quantum corrections.

We probe the multipartite entanglement structure of the vacuum state of a CFT in 1+1 dimensions, using recovery operations that attempt to reconstruct the density matrix in some region from its reduced density matrices on smaller subregions. We use an explicit recovery channel known as the twirled Petz map, and study distance measures such as the fidelity, relative entropy, and trace distance between the original state and the recovered state. One setup we study in detail involves three contiguous intervals A, B and C on a spatial slice, where we can view these quantities as measuring correlations between A and C that are not mediated by the region B that lies between them. We show that each of the distance measures is both UV finite and independent of the operator content of the CFT, and hence depends only on the central charge and the cross-ratio of the intervals. We evaluate these universal quantities numerically using lattice simulations in critical spin chain models, and derive their analytic forms in the limit where A and C are close using the OPE expansion. We also compare the mutual information between various subsystems in the original and recovered states, which leads to a more qualitative understanding of the differences between them. Further, we introduce generalizations of the recovery operation to more than three adjacent intervals, for which the fidelity is again universal with respect to the operator content.

We describe supersymmetric SYK models which display a scaling similarity at low temperatures, rather than the usual conformal behavior. We discuss the large N equations, which were studied previously as uncontrolled approximations to other models. We also present a picture for the physics of the model which suggest that the relevant low energy degrees of freedom are almost free. We also searched for a spin glass phase but we found no replica symmetry breaking solutions.

We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) horizon, the mere presence of the horizon will eventually destroy the coherence of the superposition in a finite time. This occurs because, in effect, the long-range fields sourced by the superposition register on the black hole horizon which forces the emission of entangling “soft gravitons/photons” through the horizon. This enables the horizon to harvest “which path” information about the superposition. We provide estimates of the decoherence time for such quantum superpositions in the presence of a black hole and cosmological horizon. Finally, we further sharpen and generalize this mechanism by recasting the gedankenexperiment in the language of (approximate) quantum error correction. This yields a complementary picture where the decoherence is due to an “eavesdropper” (Eve) in the black hole attempting to obtain "which path" information by measuring the long-range fields of the superposed body. We explicitly compute the quantum fidelity to determine the amount of information such an Eve can obtain and show, by the information-disturbance tradeoff, a direct relationship between the information gained by Eve and the decoherence of the superposition in the exterior. In particular, we show that the decoherence of the superposition corresponds to the "optimal" measurement made by Eve in the black hole interior.

We quantize JT gravity with matter on the spatial interval with two asymptotically AdS boundaries. We consider the von Neumann algebra generated by the right Hamiltonian and the gravitationally dressed matter operators on the right boundary. We prove that the commutant of this algebra is the analogously defined left boundary algebra and that both algebras are type II infinity factors. These algebras provide a precise notion of the entanglement wedge away from the semiclassical limit.

We argue that generic local subregions in semiclassical quantum gravity are associated with von Neumann algebras of type II_1, extending recent work by Chandrasekaran et.al. beyond subregions bounded by Killing horizons. The subregion algebra arises as a crossed product of the type III_1 algebra of quantum fields in the subregion by the flow generated by a gravitational constraint operator. We conjecture that this flow agrees with the vacuum modular flow sufficiently well to conclude that the resulting algebra is type II_\infty, which projects to a type II_1 algebra after imposing a positive energy condition. The entropy of semiclassical states on this algebra can be computed and shown to agree with the generalized entropy by appealing to a first law of local subregions. The existence of a maximal entropy state for the type II_1 algebra is further shown to imply a version of Jacobson’s entanglement equilibrium hypothesis. We discuss other applications of this construction to quantum gravity and holography, including the quantum extremal surface prescription and the quantum focusing conjecture.

In holography, the quantum extremal surface formula relates the entropy of a boundary state to the sum of two terms: the area term and the entropy of bulk fields inside the entanglement wedge. As the bulk effective field theory suffers from UV divergences, the second term must be regularized. It has been conjectured since the work of Susskind and Uglum that the renormalization of Newton’s constant in the area term exactly cancels the difference between different choices of regularization for bulk entropy. In this talk, I will explain how the recent developments on von Neumann algebras appearing in the large N limit of holography allow to prove this claim within the framework of holographic quantum error correction, and to reinterpret it as an instance of the ER=EPR paradigm. This talk is based on the paper arXiv:2302.01938.

There are several suggestions for an appropriate entry for quantum complexity in the holographic duality dictionary. The question is which notion of complexity and what is the precise duality. In this talk I endeavor to answer exactly this question for one, well studied, system. Krylov complexity has the signatures of quantum complexity at all time scales; it can be defined for operators or states. I will describe some of its features and show that in the setup of 2-dimensional JT gravity, Krylov complexity computed on the boundary has a well defined, precise geometrical meaning in the bulk.

A long-standing problem in QFT and quantum gravity is the construction of an “IR-finite” S-matrix. Infrared divergences in scattering theory are intimately tied to the “memory effect” and the existence of an infinite number of “large gauge charges”. A suitable “IR finite” S-matrix requires the inclusion of states with memory (which do not lie in the standard Fock space). For QED such a construction was achieved by Faddeev and Kulish by appropriately “dressing” charged particles with memory. However, we show that this construction fails in the case of massless QED, Yang-Mills theories, linearized quantum gravity with massless/massive sources, and in full quantum gravity. In the case of quantum gravity, we prove that the only "Faddeev-Kulish" state is the vacuum state. We also show that non-Faddeev Kulish representations are also unsatisfactory. Thus, in general, it appears there is no preferred Hilbert space for scattering in QFT and quantum gravity. Nevertheless we show how scattering can be formulated in a manner that manifestly IR-finite without any “ad-hoc” restrictions or dressing on the states. Finally, we investigate the consequences of the superselection due to the “large gauge charges” and illustrate that, in QED, nearly all scattering states are completely decohered in the bulk.