L2

Recent years have seen the expansion of the traditional notion of symmetry in quantum theory to so-called generalised or categorical symmetries, which may in particular be non-invertible. This seems to be at odds with Wigner's theorem, which asserts that quantum symmetries ought to be implemented by (anti)unitary -- and hence invertible -- operators on the Hilbert space. In this talk, we will try to resolve this puzzle for generalised symmetries that are described by (higher) fusion categories. After giving a gentle introduction to the latter, we will discuss how one can associate an inner-product-preserving operator to (possibly non-invertible) symmetry defects and illustrate our construction through concrete examples. Based on the recent work 2602.07110 with Gai and Schäfer-Nameki.

In this talk, I will examine the dynamics of the fermion–rotor system, originally introduced by Polchinski as a toy model for monopole–fermion scattering. Despite its simplicity, the system is surprisingly subtle, with ingoing and outgoing fermion fields carrying different quantum numbers. I will show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries, thereby resolving the long-standing Unitarity puzzle. I will then discuss generalizations of this setup with multiple rotors and unequal charges, and demonstrate how the system can be viewed as a UV-completion of boundary states for chiral theories, establishing a connection to the proposed resolution of the puzzle using boundary conformal field theory.

In this seminar, I will explore how the sum over topologies in pure AdS_3​ quantum gravity furnishes a consistent statistical interpretation of the boundary CFT_2. By formulating a statistical version of the conformal bootstrap, which combines crossing symmetry with typicality at high energies, we will discover a large set of non-handlebody topologies in the bulk (of which I will give some examples) that are needed for consistency of the boundary description. Interestingly, this set contains only on-shell (i.e. hyperbolic) 3-manifolds, but not all of them. This suggests that the full sum over all on-shell saddles in 3d gravity may be a highly non-minimal solution of the statistical bootstrap. Based on the recent work 2601.07906 with Belin, Collier, Eberhardt and Liska.

Energy correlations characterise the energy flux through detectors at infinity produced in a collision event. In CFTs, these detectors are examples of light-ray operators and, in particular, the stress tensor operator integrated over future null infinity. In N=4 SU(N_c) SYM, we combine perturbation theory, holography, integrability, supersymmetric localisation, and modern conformal bootstrap techniques to obtain predictions for such a collider experiment at finite coupling, both at finite number of colours, and in the planar limit. In QCD, the coupling runs with the angle between detectors, and there is a transition from perturbative to non-perturbative QCD. In N=4 SYM, a similar transition occurs when the coupling is varied, which we explore quantitatively. I will describe the physics underlying this observable and some of the methods used, particularly in regimes with analytical control.

It is well known to mathematicians that there is a deep relationship between the arithmetic of algebraic varieties and their geometry.