Holographic baryons and instanton crystals

Abstract

In a wide class of holographic models, like the one proposed by Sakai and Sugimoto, baryons can be approximated by instantons of non-Abelian gauge fields that live on the world-volume of flavor D-branes. In the leading order, those are just the Yang-Mills instantons, whose solutions can be constructed from the celebrated Atiyah-Drinfeld-Hitchin-Manin (ADHM) construction. This fact can be used to study various properties of baryons in the holographic limit. In particular, one can attempt to construct a holographic description of the cold dense nuclear matter phase of baryons. It can be argued that holographic baryons in such a regime are necessarily in a solid crystalline phase. In this review, we summarize the known results on the construction and phases of crystals of the holographic baryons. Keywords: Cold dense nuclear matter; Sakai-Sugimoto model; holographic baryons; instantons. * Corresponding author. 1540052-1 Mod. Phys. Lett. B 2015.29. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SANTA BARBARA on 08/23/15. For personal use only. V. Kaplunovsky, D. Melnikov & J. Sonnenschein 1540052-4 Mod. Phys. Lett. B 2015.29. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SANTA BARBARA on 08/23/15. For personal use only. Holographic baryons and instanton crystalsdistances between the baryons, the repulsion is due to the fact that the lightest isoscalar vector, whose exchange yields repulsion, is lighter than the lightest scalar that yields attraction. In the near and intermediate zones, the interaction between two instantons of the SS model is purely repulsive. By using the gSS instead of the SS model, the severeness of the problem can be reduced. As was shown in Ref. 28 in the gSS (and not in the SS) model, there is, in addition to the repulsive force, also an attractive one due to an interaction of the instantons with a scalar field that associates with the fluctuation of the embedding, though the ratio of the attractive to repulsive potential can never exceed 1/9. Thus in both, the SS and the gSS nuclei will not be formed.In Ref. 37, it was shown that there is another holographic model 38 with a dominance of the attraction at long distances, but at the same time, a tiny ∼ 1.7% binding energy. In that model, the lightest scalar is in fact a pseudo-Goldstone boson associated with the spontaneous breaking of the scale symmetry. This meson can be made to be lighter, but not much lighter, than the lightest isoscalar vector and hence the emerging system is that of small attraction dominance. 37 The fact that in the gSS, the interaction between the baryons is for any separation distance repulsive will be important, but not crucial for this review, as we shall see in more detail later.Motivated by the interesting behavior of skyrmions at high density and being equipped with the new methodology of holography, in Refs. 29 and 30, the authors of this review decided to look at the problem of the cold nuclear matter from the holographic perspective. Conversely to the real nuclear m...

From Kepler problem to skyrmions

“…Then, this very description is quite close to a successful theory of the nuclear matter -the Skyrme theory (for alternative interpretations of this theory, see Refs. [28][29][30][31][32]. Only the nuclear matter, and probably the matter in general should be described not by an Euclidean geometry but by a Lobachevsky geometry.…”

Baryon superfluids in AdS/CFT with flavor

“…In order to describe baryonic matter one needs to study multi-soliton solutions [16][17][18][19] or use a phenomenological approach if one is interested in homogeneous states [20][21][22][23][24][25][26][27][28][29], with the drawback that the physical properties of the state depends on the assumptions one needs to make. Furthermore, stable soliton solutions have sizes that are typically of the order of the string scale [14], thus casting doubts on the validity of the brane action used to find those solutions.…”

“…Then (4.14) becomes 19) so the coefficient of ∂ ρ V is ∂ ρ K/K. Then, the solution for the first derivative is…”

Nuclear states and spectra in holographic QCD

“…1 Holographic deuteron was also studied [18,25,26] (see also [27,28]). The soliton picture has been extended to the study of infinite systems, with a finite baryon density [29,30,31,32,33,34].…”