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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.

I will review some recent developments that attempt to put modern mathematical tools and structural insights to effective use in physics. The focus will be on two such tools. The first is a perspective on superspace geometry that leads to powerful structural analogies between twisted theories (which encode the dynamics of particular BPS subsectors) and their untwisted parents. The second deals with generalizations of typical field theories akin to the generalization from symplectic to Poisson phase spaces. As an application, one obtains an object with N=(2,0) superconformal symmetry in six dimensions. Working at the holomorphic level on flat space, this object becomes the current algebra of the exceptional simple superalgebra E(3|6), which localizes to the W_2 algebra and dimensionally reduces to sl(2) super Yang-Mills theory. This is a mixture of joint work with numerous collaborators, in particular Hahner, Raghavendran, and Williams.