abstract

In these lectures, we present the behavior of conventional $\overline{q}q$ mesons, glueballs, and hybrids in the large-$N_c$ limit of QCD. To this end, we use an approach based on rather simple “NJL-like” bound-state equations. The obtained large-$N_c$ scaling laws are general and coincide with the known results. A series of consequences, such as the narrowness of certain mesons and the smallness of some interaction types, the behavior of chiral and dilaton models at large $N_c,$ and the relation to the compositeness condition and the standard derivation of large-$N_c$ results, are explained. The bound-state formalism shows also that mesonic molecular and dynamically generated states do not form in the large-$N_c$ limit. The same fate seems to apply also to tetraquark states, but here further studies are needed. Next, following the same approach, baryons are studied as bound states of a generalized diquark ($N_c-1$ antisymmetric object) and a quark. Similarities and differences with regular mesons are discussed. All the standard scaling laws for baryons and their interaction with mesons are correctly reproduced. The behavior of chiral models involving baryons and describing chirally invariant mass generation is investigated. Finally, properties of QCD in the medium at large$N_c$ are studied: the deconfinement phase transition is investigated along the temperature and the chemical potential directions, respectively. While the critical temperature for deconfinement $T_{\mathrm{dec}}$ is $N_c$-independent$,$ the critical chemical potential is not and increases for growing $N_c,$ thus for very large $N_c$, one has confined matter below $T_{\mathrm{dec}}$ and deconfined above. Yet, in the confined phase but for large densities, one has a ‘stiff-matter’ phase whose pressure is proportional to $N_c$ (just as a gas of quarks would do) in agreement with a quarkyonic phase. Within the QCD phase diagrams, the features of different models at large$N_c$ are reviewed and the location of the critical endpoint is discussed. In the end, the very existence of nuclei and the implications of large-$N_c$ arguments for neutron stars are outlined.

abstract

In these lecture notes, I review how to use large-$N$ techniques to solve quantum field theories in various dimensions. In particular, the case of $N$‑dimensional quantum mechanics, non-relativistic cold and dense neutron matter, and scalar field theory in four dimensions are covered. A recurring theme is that large-$N$ solutions are fully non-perturbative, and can be used to reliably access quantum field theory for parameter regions where weak-coupling expansions simply fail.

abstract

According to the Color Glass Condensate approach to relativistic heavy-ion collisions, the earliest phase of the collision is a glasma which is made of highly populated gluon fields that can be treated classically. Using a proper time expansion, we study analytically various properties of the glasma. In particular, we compute the glasma energy-momentum tensor which allows us to obtain the energy density, longitudinal and transverse pressure, collective flow, and angular momentum. We also study the role of the glasma in jet quenching by computing collisional energy loss and transverse momentum broadening.

abstract

Understanding the properties and physical phase of the dense strongly interacting matter present in the cores of neutron stars or created in their binary mergers remains one of the most prominent open problems in nuclear astrophysics. While most microscopic analyses have historically relied on solvable phenomenological models of nuclear and quark matter, in recent years a model-independent approach utilizing only controlled ab-initio calculations and astrophysical observations has emerged as a viable alternative.
In these lecture notes, I review recent progress in first-principles weak-coupling calculations within high-density quark matter, shedding light on its thermodynamic and transport properties. I cover the most important technical tools used in such calculations, introduce selected highlight results, and explain how this information can be used in phenomenological studies of neutron-star physics. The notes do not offer a self-consistent treatment of the topics covered, but rather aim at filling gaps in existing textbooks on thermal field theory and at connecting the dots in a story developed in several recent research articles, to which the interested reader is directed for further technical details.