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Many Phases of Generalized 3D Instanton Crystals

by Matti Jarvinen, Vadim Kaplunovsky, Jacob Sonnenschein

Submission summary

As Contributors: Matti Jarvinen
Arxiv Link: (pdf)
Date accepted: 2021-07-02
Date submitted: 2021-06-21 08:00
Submitted by: Jarvinen, Matti
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • High-Energy Physics - Phenomenology
  • Nuclear Physics - Theory
Approaches: Theoretical, Computational


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. In this article we initiate the analysis of the three-dimensional crystal structures and the orientation patterns for the two-body potential that follows from holographic duality. The outcome of the analysis includes several unexpected results. We perform simulations of ensembles of O(10000) instantons whereby we identify the lattice structure and orientations for the different values of the weight factors of the non-Abelian orientation terms in 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 latter include variants of face-centered-cubic, hexagonal, and simple cubic crystals which may have remarkably large or small aspect ratios. 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 allows us to precisely determine the structure of the phase diagram.

Published as SciPost Phys. 11, 018 (2021)

Author comments upon resubmission

We thank the referees for carefully reading the manuscript and for relevant comments that helped us to improve its quality.

The new version takes into account all comments of the invited referees, and fixed a few minor issues that we noticed ourselves. Please see the responses to the referee reports and the list of changes for details.

List of changes

The page and equation numbering in this list refers to the new (second) version of the manuscript.

- We added a comment on the dimensionality of the crystals considered in the article in the last paragraph of page 3, before Eq. (1).
- We revised the discussion of the external force in the third paragraph of page 4, and also modified the first item of the list in the fourth (last) paragraph on the same page, which contained an imprecise statement of the force.
- We added a comment that detailed definitions will be given in Sec. 5 in the first item (oriented non-Abelian phase) of the second bulleted list on page 5.
- We added the definition of bcc in the same item, near the end of page 5.
- We added a comment on the nature and dimensionality of the instanton system in the first sentence of Sec. 2, end of page 6.
- We added a discussion on how the two-body potential arises from the WSS model in the last paragraph of page 7. This includes the new Eq. (4).
- We added a new paragraph at the end of Sec. 2.2, page 8, which discusses the interpretation of the parameters alpha and beta.
- We added a comment on the external force and link to Appendix A.2, where it is discussed in detail, in the first paragraph of Sec. 3, on page 9.
- We added a reminder that the details of the phase diagram will be discussed in Secs. 4 and 5 in the first paragraph of Sec. 3.3, near the end of page 12.
- We added a clarifying comment on the rapid convergence in the spherical phases in the first paragraph of Sec. 3.4, on page 15.
- We added a new paragraph discussing the choice of external force and on the various checks we have carried out in the spherically arranged phases at the end of Sec. 3.4, on page 16.
- We removed an incomplete sentence in Sec. 5.1, page 29, right after Eq. (66).
- We added a new paragraph which points out how the parameter dependence of the phase diagram reflects the changes in the two-body potential at the end of Sec. 5, on page 34.
- We introduced new subsections titles (A.1 and A.2) in Appendix A so that we can refer to the discussion of the external force in Appendix A.2 more precisely.
- We thoroughly revised Appendix B, adding several clarifying comments, cross links, and discussion on tricky points in the simulation.

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