Vector dominance, one flavored baryons, and QCD domain walls from the "hidden" Wess-Zumino term
09 Jun 2021-Vol. 10, Iss: 6, pp 138
TL;DR: In this article, it was shown 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.
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.
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TL;DR: In this article, the authors discuss the sheet structure of compressed baryonic matter possibly present in massive compact stars in terms of quantum Hall droplets and skyrmions for baryons in medium.
Abstract: We discuss the "sheet structure" of compressed baryonic matter possibly present in massive compact stars in terms of quantum Hall droplets and skyrmions for baryons in medium. The theoretical framework is anchored on a generalized scale symmetric hidden local symmetry that encompasses standard nuclear effective field theory ($s$EFT) and can access the density regimes relevant to massive compact stars. It hints at a basically different, hitherto unexplored structure of the {\it densest} baryonic matter stable against collapse to black hole. Hidden scale symmetry and hidden local symmetry together in nuclear effective field theory are seen to play a potentially crucial role in providing the hadron-quark duality in compressed baryonic matter.
17 citations
TL;DR: In this paper, a new development on the possible direct connection between the topological structure of the Nf=1 baryon as a FQH droplet and that of the nf≥2 baryons (such as nucleons and hyperons) as skyrmions was made.
Abstract: We review a new development on the possible direct connection between the topological structure of the Nf=1 baryon as a FQH droplet and that of the Nf≥2 baryons (such as nucleons and hyperons) as skyrmions. This development suggests a possible “domain-wall (DW)” structure of compressed baryonic matter at high density expected to be found in the core of massive compact stars. Our theoretical framework is anchored on an effective nuclear effective field theory that incorporates two symmetries either hidden in the vacuum in QCD or emergent from strong nuclear correlations. It presents a basically different, hitherto undiscovered structure of nuclear matter at low as well as high densities. Hidden “genuine dilaton (GD)” symmetry and hidden local symmetry (HLS) gauge-equivalent at low density to nonlinear sigma model capturing chiral symmetry, put together in nuclear effective field theory, are seen to play an increasingly important role in providing hadron–quark duality in baryonic matter. It is argued that the FQH droplets could actually figure essentially in the properties of the vector mesons endowed with HLS near chiral restoration. This strongly motivates incorporating both symmetries in formulating “first-principles” approaches to nuclear dynamics encompassing from the nuclear matter density to the highest density stable in the Universe.
7 citations
KEK1
TL;DR: In this article, a domain-wall configuration of the meson bounded by a Hall droplet is proposed to describe the baryons with spin $N_c/2.
Abstract: A domain-wall configuration of the $\eta'$ meson bounded by a string (called a pancake or a Hall droplet) is recently proposed to describe the baryons with spin $N_c/2$. In order to understand its baryon number as well as the flavor quantum number, we argue that the vector mesons (the $\rho$ and $\omega$ mesons) should play an essential role for the consistency of the whole picture. We determine the effective theory of large-$N_c$ QCD with $N_f$ massless fermions by taking into account a mixed anomaly involving the $\theta$-periodicity and the global symmetry. The anomaly matching requires the presence of a dynamical domain wall on which a $U(N_f)_{-N_c}$ Chern-Simons theory is supported. We consider the boundary conditions that should be imposed on the edge of the domain wall, and conclude that there should be a boundary term that couples the $U(N_f)_{-N_c}$ gauge field to the vector mesons. We discuss the impact on physics of the chiral phase transition and the relation to the "duality" of QCD.
6 citations
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TL;DR: In this article, the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a meson.
Abstract: To study a nuclear system in the Skyrme model one must first construct a space of low energy Skyrme configurations. However, there is no mathematical definition of this configuration space and there is not even consensus on its fundamental properties, such as its dimension. Here, we propose that the full instanton moduli space can be used to construct a consistent skyrmion configuration space, provided that the Skyrme model is coupled to a meson. Each instanton generates a unique skyrmion and we reinterpret the 8N instanton moduli as physical degrees of freedom in the Skyrme model. In this picture a single skyrmion has six zero modes and two non-zero modes: one controls the overall scale of the solution and one the relative size of the Skyrme and meson fields. We study the N=1 and N=2 systems in detail. Two interacting skyrmions can excite the meson field through scattering, suggesting that the meson and Skyrme fields are intrinsically linked. Our proposal is the first consistent manifold description of the two-skyrmion configuration space. The method can also be generalised to higher N and thus provides a general framework to study any skyrmion configuration space.
4 citations
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TL;DR: In this article, the authors describe the on-going effort to formulate the baryon-quark continuity in terms of a topology change in the equation of state (EoS) of dense baryonic matter in analogy to the mapping of the characteristics of Chern-Simon topological field theory to Kohn-Sham density functional theory in the fractional quantized Hall effect.
Abstract: We describe the on-going effort to formulate the baryon-quark continuity in terms of a topology change in the equation of state (EoS) of dense baryonic matter in analogy to -- and inspired by -- the mapping of the characteristics of Chern-Simon topological field theory to Kohn-Sham density functional theory in the fractional quantized Hall effect (FQHE). This is done by translating the density-dependent characteristics of the skyrmion-half-skyrmion transition formulated in the presence of hidden local symmetry and (hidden) scale symmetry to the density-dependent parameters of a renormalization-group approach to Fermi-liquid fixed point theory. Predictions made in finite nuclei and infinite compact-star matter are presented.
3 citations
References
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2,450 citations
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TL;DR: In this paper, the U(1) problem is reconsidered from the point of view of the 1 N expansion, and it is argued that various heuristic ideas about the η′ are valid from this view.
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TL;DR: The approximate {ital in}{minus}{ital medium} scaling law is established, which has a highly nontrivial implication for nuclear processes at and above nuclear-matter density.
Abstract: By using effective chiral Lagrangians with a suitable incorporation of the scaling property of QCD, we establish the approximate in-medium scaling law, ${\mathit{m}}_{\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$/${\mathit{m}}_{\mathrm{\ensuremath{\sigma}}}$\ensuremath{\approxeq}${\mathit{m}}_{\mathrm{N}}^{\mathrm{*}}$/${\mathit{m}}_{\mathrm{N}}$ \ensuremath{\approxeq}${\mathit{m}}_{\mathrm{\ensuremath{\rho}}}^{\mathrm{*}}$/${\mathit{m}}_{\mathrm{\ensuremath{\rho}}}$\ensuremath{\approxeq}${\mathit{m}}_{\mathrm{\ensuremath{\omega}}}^{\mathrm{*}}$/${\mathit{m}}_{\mathrm{\ensuremath{\omega}}}$\ensuremath{\approxeq}${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$/${\mathit{f}}_{\mathrm{\ensuremath{\pi}}}$. This has a highly nontrivial implication for nuclear processes at and above nuclear-matter density. Some concrete cases are cited in this paper.
1,049 citations