We study the quantum Ising model on (2+1)-dimensional anti-de Sitter space using Matrix Product States (MPS) and Matrix Product Operators (MPOs). Our spatial lattices correspond to regular tessellations of hyperbolic space with coordination number seven. We find the ground state of this model using the Density Matrix Renormalization Group (DMRG) algorithm which allowed us to probe lattices that range in size up to 232 sites. We explore the bulk phase diagram of the theory and find disordered and ordered phases separated by a phase transition. We find that the boundary-boundary spin correlation function exhibits power law scaling deep in the disordered phase of the Ising model consistent with the anti-de Sitter background. By tracing out the bulk indices, we are able to compute the density matrix for the boundary theory. At the critical point, we find the entanglement entropy exhibits the logarithmic dependence of boundary length expected for a one-dimensional CFT but away from this, we see a linear scaling. In comparison, the full system exhibits a volume law scaling, which is expected in chaotic and highly connected systems. We also measure Out-of-time-Ordered-Correlators (OTOCs) to explore the scrambling behavior of the theory.

We present updated results for the hadronic light-by-light (HLbL) contribution to the muon anomalous magnetic moment. The calculations are based on ETMC's $N_f=2+1+1$ Wilson-clover twisted-mass ensembles at the physical point. We perform continuum extrapolations for the strange- and charm-quark connected contributions and report on our results for the light-quark connected and light-quark 2+2 disconnected contributions at one lattice spacing.

We study four-dimensional conformal field theories (CFTs) with an abelian $U(1)$ global symmetry using the conformal bootstrap approach. We obtain numerical bounds on the scaling dimensions of low-lying operators, the stress-tensor central charge, and a particular combination of the 't Hooft anomaly and the current central charge. Our analysis provides the first non-perturbative constraints on four-dimensional CFTs with conserved abelian currents and establishes a framework that can be extended to theories with non-abelian global symmetries.

Using the framework of generalized parton distribution, we provide a unified interpretation of the connected and disconnected contributions from the ab-initio Euclidean path-integral formulation of the hadronic tensor in both the nucleon elastic form factors and the parton distribution functions. We develop a phenomenology to elucidate non-perturbative contributions to deep inelastic structure functions, which can be extended to observables in heavy-ion collisions probing baryon junctions.

In relativistic field theories, the mass spectrum is given by the difference between the energy of the vacuum and the excited states. Near the continuum limit, the cancellation between these two values leads to loss of precision. We propose a method to extract the mass gap directly using quantum computers and apply it to a particular version of the nonlinear $\sigma$-model with the correct continuum limit and perform calculations in quantum hardware (at strong coupling) and simulation in classical computers (at weak coupling).