Abstract
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 ∝ \( M_2^2x_2^2+M_3^2x_2^2+M_4^2x_4^2 \), 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 \( {{\mathbb{Z}}_2} \), Klein, prismatic, or dihedral subgroup of the \( {{{\mathrm{SU}(2)}} \left/ {{{{\mathbb{Z}}_2}}} \right.} \), 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.
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Kaplunovsky, V., Sonnenschein, J. Dimension changing phase transitions in instanton crystals. J. High Energ. Phys. 2014, 22 (2014). https://doi.org/10.1007/JHEP04(2014)022
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DOI: https://doi.org/10.1007/JHEP04(2014)022