Dimension changing phase transitions in instanton crystals

Vadim Kaplunovsky, Jacob Sonnenschein

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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 ∝M22x22+M 32x22,+M4 2x42 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 ℤ2, Klein, prismatic, or dihedral subgroup of the (2)ℤ2, 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.

Original languageEnglish
Article number22
JournalJournal of High Energy Physics
Issue number4
StatePublished - Apr 2014


  • AdS-CFT Correspondence
  • Holography and condensed matter physics (AdS/CMT)
  • Phase Diagram of QCD


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