Holographic baryons and instanton crystals

In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-Abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang–Mills instantons, whose solutions can be constructed from the celebrated Atiyah–Drinfeld–Hitchin–Manin (ADHM) construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review, we summarize the known results on the construction and phases of crystals of the holographic baryons.