# Ryan Weller: Fun with large N

Large-N quantum field theories are a playground for doing non-perturbative physics. Certain large-N theories turn out to be asymptotically free in d=4 and have features like bound states, just like quantum chromodynamics (QCD) and Yang–Mills theories. Their asymptotic freedom is connected to their apparent non-Hermiticity. However, when coupled with an antilinear symmetry, in many cases referred to as PT symmetry, this non-Hermicity does not prevent such theories from having real, bounded spectra and a notion of unitarity. It’s possible to calculate equations of state, phase diagrams, and transport coefficients like shear viscosity η/s in these theories. I will talk in particular about the O(N) model, which is relevant to Higgs physics when N=4. I’ll discuss the phase structure at large N. There is a first-order phase transition at finite temperature, which has implications for cosmology. In particular, the stable vacuum is not the spontaneous symmetry broken (SSB) vacuum, as is otherwise assumed in the Standard Model of particle physics. I’ll demonstrate how one can generate “mass from nothing”, without SSB, when a massless Higgs field is coupled to a U(1) Abelian gauge field. Lastly, I’ll briefly talk about how large-N techniques in the O(N) model are analogous to a method for non-perturbative analytical calculations in QCD and Yang–Mills theories, via so-called Rn resummation methods. This analogy might allow a study of the phase structure, transport coefficients, and confinement in QCD and Yang–Mills, with applications to the quark–gluon plasma and neutron stars.