Large Nc Baryons and Baryonic Matter with Heavy Quarks

Abstract

In this dissertation, Quantum Chromodynamics (QCD) is explored at finite baryon density in a combined heavy quark and 't Hooft large Nc limit of QCD. Non-relativistic baryons are fully antisymmetric states containing Nc quarks; it was proposed by Witten that baryons can be described through a mean-field picture in which each quark moves in an average potential created by the remaining Nc − 1 quarks. A proof of this mean-field picture is constructed here. Additionally, the mean-field baryon problem is also considered in one spatial dimension, where the full relativistic baryon problem has been solved independently by Bringoltz. The ground state properties of single, isolated baryons and baryonic matter in 1+1 dimension is calculated using Witten's mean-field method and compared against the results of the Bringoltz method. Finally, saturated nuclear matter is studied in the combined limit in 3+1 dimensions, where the density of saturated nuclear matter is calculated.