Seminars

Recently, a matrix formulation of a three-dimensional quantum space was proposed. The basic idea is that (in)finite number of fuzzy spheres can be glued together in a specific way. During the seminar, we will discuss the construction of the model with some recent examples from field theory, quantum mechanics and classical physics.

The AdS/CFT correspondence is a duality stating that quantum gravity in an AdS spacetime is equivalent to a conformal field theory (CFT) on its boundary. Its development has been a central topic in theoretical physics for the past 25 years. However, its extension to non-AdS backgrounds, such as flat space, remains challenging. A recent proposal suggests that 4D quantum gravity in flat space could be dual to a 2D celestial CFT on the sphere. The discovery of deep connections between Weinberg’s soft theorems and asymptotic charge conservation established a direct link between bulk soft operators and celestial CFT symmetry generators, including the stress tensor. This led to the computation of the CCFT central charge, which was found to be zero. Since a unitary CFT with vanishing central charge is trivial, alternative nontrivial CFTs must be considered. One such class is logarithmic CFTs (LCFTs), characterized by logarithmic behavior in correlation functions. In our work, we analyzed the field content of CCFT and found that two specific infrared bulk modes form a logarithmic CFT doublet. We discuss this result in relation to previous observations of logarithmic structures in the IR-finite part of celestial OPEs.

Motivated by group-theoretical questions that arise in the context of asymptotic symmetries in gravity, we study model spaces and their quantization from the viewpoint of constrained Hamiltonian systems. More precisely, we propose a definition of a model space for a generic Lie group G as a suitable second class constrained system associated to the cotangent bundle $T^{*}G$. Before turning to the non-compact infinite-dimensional groups relevant in the gravitational setting, we work out all details in the simplest case of $\mathrm{SU}(2)$. Besides recovering well-known results on the quantum theory of angular momentum from a unified perspective, the analysis sheds some light on the definition and properties of spin-weighted/monopole spherical harmonics.