Dimension Changing Phase Transitions in Instanton Crystals

TL;DR

This paper explores the phase transitions of instanton lattices in lower dimensions, revealing various orientation patterns and phase diagrams, with implications for understanding baryonic and quarkyonic phases in nuclear matter.

Contribution

It introduces a numeric approach to analyze instanton orientation patterns in lower-dimensional lattices, uncovering diverse phases and transition types without assuming specific ansatzes.

Findings

Identified multiple orientation phases including Z_2, Klein, prismatic, and dihedral groups.

Mapped phase diagrams showing first- and second-order transitions.

Demonstrated dominance of two-body forces at low to moderate densities.

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 Z_2, Klein, prismatic, or dihedral subgroup of the SU(2)/Z_2, 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 diagram 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.