Baryons, salt and popcorn in holographic QCD

The Sakai-Sugimoto model is the leading model of holographic QCD. It has an effective five-dimensional description in which baryons correspond to the bulk topological solitons of a Yang-Mills-Chern-Simons theory. However, the large dimensionality of the model means studying soliton solutions either analytically or numerically is difficult. Sakai-Sugimoto solitons in the high density limit should provide an analogue of cold, dense QCD. Two competing theories for high-density solutions are the dyon salt model, in which the appropriate crystal is a salt-like arrangement of dyons, and the baryonic popcorn model in which a series of transitions occurs where the three-dimensional soliton crystal develops extra layers in the holographic direction. In this thesis we consider a range of low-dimensional analogues and approximations to the Sakai-Sugimoto model. We first investigate an O(3) sigma model stabilised by vector mesons, and a baby Skyrme model in pure AdS spacetime, before moving on to consider homogeneous ansätze in both the holographic baby Skyrme and full Sakai- Sugimoto models. In each case we look for analogues of the dyon salt and baryonic popcorn configurations, and find evidence for new features in the high-density regime of holographic QCD.