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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.

To define an algebra of observables in quantum gravity in a way that is universal and does not depend on a background spacetime, one can consider the observables along the worldline of an observer, rather than the observables in a region of spacetime.

After reflecting on the fruitful connections between quantum information and quantum gravity, I'll discuss recent results about using classical and quantum machine learning to predict the properties of quantum systems.

String amplitudes famously accomplish several extraordinary and interrelated mathematical feats, including an infinite spin tower, tame UV behavior, and dual resonance: the ability of the amplitude to be represented as a sum over a single scattering channel. But how unique are these properties to string amplitudes? In this talk, I will demonstrate that it is possible to construct infinite new classes of tree-level, dual resonant amplitudes with customizable, non-Regge mass spectra. Crucial ingredients are Galois theory and a particular dlog transformation of the Veneziano amplitude. The formalism generalizes naturally to n-point scattering and allows for a worldsheet-like integral representation. In the case of a Regge spectrum, I will investigate whether the structure of the Veneziano amplitude can be bootstrapped from first principles. Even there, we will find that there is extra freedom in the dynamics, allowing for a new class of dual resonant hypergeometric amplitudes with a linear spectrum.

In order to derive the classical string action from the worldsheet, it is necessary to take string theory off shell. This can be done by a prescription of Tseytlin, who proposed taking the worldsheet sphere QFT partition function and *differentiating* it with the log of the UV cutoff. I will explain why this strange prescription always gives the correct answers, for both the S-matrix and equations of motion, to all orders in perturbation theory. I will also compare the Susskind-Uglum off-shell method of calculating black hole entropy, to the more popular (but also more dubious) orbifold method. Based on work with Amr Ahmadain (arXiv:2211.08607 and arXiv:2211.16448).

We obtain all solutions of the Wheeler-DeWitt equation with positive cosmological constant for a closed universe in the large-volume limit. We define a natural norm on the solution space and thereby obtain a description of the Hilbert space of quantum gravity in an asymptotically de Sitter spacetime. This provides the finite G_N generalization of the Hilbert space constructed by Higuchi using group averaging. All the states in this Hilbert space share the symmetries of the Euclidean vacuum. We use this property to generalize the principle of holography of information to de Sitter space: data about cosmological correlators (defined as appropriately gauge-fixed observables) in an arbitrary small region suffices to specify them everywhere.

I will discuss the interplay between 2d de Sitter and supersymmetry in two concrete supergravity models coupled to superconformal field theories. Upon fixing a supersymmetric analogue of the Weyl gauge these theories can be viewed as supersymmetric extensions of timelike Liouville theory with N=1 and N=2 supersymmetry respectively. Supersymmetric timelike Liouville is well behaved in the UV and combines supersymmetry with a positive cosmological constant and a de Sitter saddle. The theory is amenable to a variety of techniques including systematic loop expansions and localization methods.

In this talk we will analyze renormalization group flows on d-dimensional planar defects, embedded in a D-dimensional conformal field theory. This general setup includes the case of quantum field theory with no defects ($D=d$), as well as defects of different dimensionality that are of interest in high energy and condensed matter physics. Using methods from quantum information theory, we will establish the irreversibility of renormalization group flows for defect dimensions $d \le 4$, and for all $D$. The main ingredients in the proof are strong subadditivity of the entanglement entropy, the Markov property of the conformal vacuum, and the quantum null energy condition.