By Karlhede, Kivelson, Sondhi

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4) The original chiral theory in terms of U ﬁeld can be made a gauge theory by introducing “hidden” gauge ﬁelds AµL,R . This gives rise to hidden local symmetry theory of Harada and Yamawaki [Harada and Yamawaki 2003] which makes up one of the principal parts of what is discussed in this volume. Now as mentioned above, symmetry arguments alone can lead to an arbitrary theory when one goes up in scale. When constructed bottom-up as an emergence phenomenon, the theory needs to be “ultraviolet (UV)-completed” to the fundamental theory in order to make the theory truly predictive.

Remarkably, baryons in this theory must come out as skyrmions since there are no explicit fermionic degrees of freedom. In fact, the 4-D skyrmion in an inﬁnite tower of vector mesons is just the instanton in the Euclidean 4-D of the 5-D Yang-Mills Lagrangian. This then elevates the skyrmion to a higher level of sophistication. Quark-hadron continuity The above discussion hints at a web of continuity between QCD degrees of freedom and hadronic degrees of freedom in free space. Now going to medium, there are another web of dualities that emerge from the dynamics.

In fact, it suggests that there can be many ways to explain the spin problem, some more in line with QCD than others. It is possible that some are correct and related to each other. Whether or not one or more explanations of a particular class are conﬁrmed by experiments in disfavor of others is not clear. 1). We write the axial current Aµ (≡ J5µ ) in the CBM as a sum of two terms, one from the interior of the bag and the other from the outside populated by the meson ﬁeld 9 The baryon charge is conserved with QV¯ = B (θ π − sin θ cos θ) for baryon number B.