Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term

Abstract

We further explore a recent proposal that the vector mesons in QCD have a special role as Chern-Simons fields on various QCD objects such as domain walls and the one flavored baryons. We compute contributions to domain wall theories and to the baryon current coming from a generalized Wess-Zumino term including vector mesons. The conditions that lead to the expected Chern-Simons terms and the correct spectrum of baryons, coincide with the conditions for vector meson dominance. This observation provides a theoretical explanation to the phenomenological principle of vector dominance, as well as an experimental evidence for the identification of vector mesons as the Chern-Simons fields. By deriving the Chern-Simons theories directly from an action, we obtain new results about QCD domain walls. One conclusion is the existence of a first order phase transition between domain walls as a function of the quarks' masses. We also discuss applications of our results to Seiberg duality between gluons and vector mesons and provide new evidence supporting the duality.

Dichotomy of Baryons as Quantum Hall Droplets and Skyrmions: Topological Structure of Dense Matter

“…This is in stark contrast with f 2 π / f 2 χ ∼ 1 which seems to be encoded in the pseudo-conformal structure in dense nuclear systems. Another notable observation is that zeroing-in on the deep IR regime associated with the η singularity involved in the domain-wall topological structure of baryons as argued in [15,16] uncovers the ω (a.k.a. Chern-Simons) mass going to zero as the fermion ("quark") mass m → ∞.…”

“…Since the gauge coupling g ρ goes to zero in approaching the vector manifestation fixed point n V M (say, n 25n 0 ) [8]), the mass m ρ ∼ f π g ρ goes to zero independently of whether or not f π goes to zero and the ρ decouples from the pions. The Lagrangian L sHLS (4) will then reduce to what was noted by Karasik [15,16]…”

“…They could be fixed by holographic QCD, but there are no known holographic QCD models that possess possible "orange" [15]-not to mention ultraviolet-completion that would allow for approaching the density above n 0 . However, as we will see later, in approaching QH droplet baryons bottom-up in density, the coefficients will be "quantized" by topology [15,16]. This takes place because there can be a phase transition from a Higgs mode to a topological phase in which the HLS fields are supposed to be (Seiberg-)dual to the gluons of QCD [24].…”

“…This is because π 3 (U(1)) = 0. The resolution to this conundrum was suggested in 2018 by Komargodski [14]: The baryon for η , while not a skyrmion soliton, turns out to be also a topological object at the large N c limit but more appropriately a fractional quantum Hall (FQH) droplet, somewhat similar to a pancake (or perhaps pita [15,16]).…”

“…In following Karasik's arguments [15,16], we take the sHLS Lagrangian (4) and focus on the terms that involve the η field in that Lagrangian. In doing this manipulation, the role of the conformal compensator present to provide (Seiberg-)duality plays the crucial role in contrast to what was conducted in [15,16] where the the role of dilaton effects is performing double trace, which is ignored. With the baryons generated as solitons in sHLS, the parameters of the Lagrangian contain the "intrinsic density dependence" (IDD) inherited from QCD at the matching between EFT and QCD.…”