Generalized 3D instanton crystals

Nuclear matter at large number of colors is necessarily in a solid phase. In particular holographic nuclear matter takes the form of a crystal of instantons of the flavor group. I analyze the three-dimensional crystal structures and the orientation patterns for the two-body potential motivated by holographic duality. I use simulations of large ensembles of instantons to identify the lattice structure and orientations for various parameter values of the two-body potential. The resulting phase diagram is surprisingly complex, including a variety of ferromagnetic and antiferromagnetic crystals with various global orientation patterns, and various "non-Abelian" crystals where orientations have no preferred direction. The simulation results are augmented by analytic analysis of the long-distance divergences, and numerical computation of the (divergence free) energy differences between the non-Abelian crystals, which precisely determine the structure of the phase diagram.