Introductory visual lecture on QCD at large-\(N_{c}\): bound states, chiral models, and phase diagram

Abstract

In these lectures, we present the behavior of conventional \(\bar{q}q\) 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 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. Next, following the same approach, baryons are studied as bound states of a generalized diquark 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. While the critical temperature for deconfinement \(T_{dec}\) is \(N_{c}\) independent\(,\) the critical chemical potential is not and increases for growing \(N_{c}\). 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.