A brief summary

Abstract

The interplay between physics and geometry has proven to be one of the most fundamental and fascinating principle in modern theoretical physics. The skyrmion as a topological soliton of the Skyrme model offers one of the early illustration of this principle whereby a non-linear cloud of bosons, pions in Skyrme’s original conception, transmute via geometry to fermions. Most if not all of fundamental field theories have exhibited this principle in a variety of forms leading to quasiparticles with topologically conserved quantum numbers. Examples are by now legion across a wide range of physical descriptions ranging from particle to solid state physics. In this special volume, we illustrate via a select set of contributions the striking recent developments across disciplines where skyrmions have emerged as fundamental objects to describe complex new non-perturbative phenomena that are robust dynamically and observed experimentally. Recent advances in holographic QCD have suggested that skyrmions are the boundary realization of instantons in a bulk supergravity theory sourced by chiral D-branes. The best realization of this holographic principle is the Sakai–Sugimoto model in the double limit of strong coupling and large number of colors. Paul Sutcliffe reviews some key aspects of this construction by critically examining the flat space self-dual approximation and its radial numerical generalization. He also expounds on new ideas brought about by the holographic principle for the multi-skyrmion problem with novel ramifications on difficult dense baryonic matter. Vadim Kaplunovsky, Dmitry Melnikov and Jacob Sonnenschein review in greater details from string theory vintage point the fascinating new world of crystals in holographic QCD whereby the bulk instantons fractionize into dyons or half-skyrmions in four-dimensional world while re-arranging under pressure or density. Cold dense matter in the large number of colors is underlined by instanton crystals that zig-zag