科研之友
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摘要
We investigate lattices of instantons and the dimension-changing transitions between them. Our ultimate goal is the 3D -> 4D transition, which is holographically dual to the phase transition between the baryonic and the quarkyonic phases of cold nuclear matter. However, in this paper (just as in [1]) we focus on lower dimensions - the 1D lattice of instantons in a harmonic potential V ae , and the zigzag-shaped lattice as a first stage of the 1D -> 2D transition. We prove that in the low- and moderate-density regimes, interactions between the instantons are dominated by two-body forces. This drastically simplifies finding the ground state of the instantons' orientations, so we made a numeric scan of the whole orientation space instead of assuming any particular ansatz. We find that depending on the M (2) /M (3) /M (4) ratios, the ground state of instanton orientations can follow a wide variety of patterns. For the straight 1D lattices, we found orientations periodically running over elements of a , Klein, prismatic, or dihedral subgroup of the , as well as irrational but link-periodic patterns. For the zigzag-shaped lattices, we detected 4 distinct orientation phases - the anti-ferromagnet, another abelian phase, and two non-abelian phases. Allowing the zigzag amplitude to vary as a function of increasing compression force, we obtained the phase diagrams for the straight and zigzag-shaped lattices in the (force, M (3) /M (4)), (chemical potential, M (3) /M (4)), and (density, M (3) /M (4)) planes. Some of the transitions between these phases are second-order while others are first-order. Our techniques can be applied to other types of non-abelian crystals.
- 出版日期2014-4-3
