The inclusion of the cosmological constant is one of the main questions faced by quantum gravity. In three dimensions, non-perturbative approaches to quantum gravity including loop quantum gravity (LQG), combinatorial quantization and spinfoam path integrals encode the cosmological constant as a deformation parameter in a quantum group structure. In this talk, I will focus on the LQG approach: I will explain the Poisson-Lie structure of the classical phase space and how its quantization naturally leads to the emergence of quantum groups. I will use the holonomy-flux algebra and its spinorial presentation introduced in the series of work by Bonzom, Dupuis, Girelli, Livine and myself. This allows to construct the Hamiltonian constraint, understand its matrix elements as Turaev-Viro amplitudes. This connects LQG to the other approaches in a unified mathematical setting.
Several anomalies have been recently reported by different laboratory experiments: the flavor anomalies involving B meson semileptonic and leptonic decays by the LHCb and B-factories, as well as the anomalous muon (g-2) by the Fermilab (g-2) collaboration. These deviations, if not coming from underestimated experimental or theoretical uncertainties, are pointing to new degrees of freedom around the few TeV scale. Enlarging the field content of the Standard Model may lead to baryon number violation, whose aggressive experimental constraints can rule out a wide range of attractive candidates. Motivated by its safeness under unacceptable baryon number violation and the possibility for having TeV scale physics, I will introduce the simplest theory for matter (leptons-quarks) unification based on the Pati-Salam symmetry and show how this theory can address both the flavor anomalies and the muon (g-2) with the scalar leptoquarks that it predicts.
A high energy muon collider complex can provide new and complementary discovery potential to the LHC or future hadron colliders. New spin-1 bosons are a motivated class of exotic new physics models. In particular leptoquarks, dark photons, and Lμ — Lτ models have distinct production channels at hadron and lepton machines. We study a vector leptoquark model at a muon collider with √ s = 3, 14 TeV within a set of both UV and phenomenologically motivated flavor scenarios. We compute which production mechanism has the greatest reach for various values of the leptoquark mass and the coupling between leptoquark and Standard Model fermions. We find that we can probe leptoquark masses up to an order of magnitude beyond √ s with perturbative couplings. Additionally, we can also probe regions of parameter space unavailable to flavor experiments. In particular, all of the parameter space of interest to explain recent low-energy anomalies in B meson decays would be covered even by a √ s = 3 TeV collider. We also consider other applications of a muon collider complex in the hunt for new physics.