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.
Cited by 2
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- 1 2 3 Matti Jarvinen,
- 4 Vadim Kaplunovsky,
- 1 Jacob Sonnenschein
- 1 אוניברסיטת תל אביב / Tel Aviv University [TAU]
- 2 Asia Pacific Center for Theoretical Physics [APCTP]
- 3 포항공과대학교 / Pohang University of Science and Technology [POSTECH]
- 4 The University of Texas at Austin [UT Austin]
- Israel Science Foundation [ISF]
- Ministry of Science and ICT, South Korea (through Organization: 대한민국 미래창조과학부 / Ministry of Science ICT and Future Planning [MSIP])
- National Research Foundation of Korea [NRF]