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Register a new userHadron physics as Seiberg dual of QCD
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Authors
Ryuichiro Kitano
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We try to identify the light hadron world as the magnetic picture of QCD. We take both phenomenological and theoretical approaches to this hypothesis, and find that the interpretation seems to show interesting consistencies. In particular, one can identify the rho and omega mesons as the magnetic gauge bosons, and the Higgs mechanism for them provides a dual picture of the color confinement.
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We sketch the basic ideas of the lattice regularization in Quantum Field Theory, the corresponding Monte Carlo simulations, and applications to Quantum Chromodynamics (QCD). This approach enables the numerical measurement of observables at the non-perturbative level. We comment on selected results, with a focus on hadron masses and the link to Chiral Perturbation Theory. At last we address two outstanding issues: topological freezing and the sign problem.
When one of the space-time dimension is compactified on $S^1$, the QCD exhibits the chiral phase transition at some critical radius. When we further turn on a background $theta$ term which depends on the $S^1$ compactified coordinate, a topological ordered phase appears at low energy via the winding of $theta$. We discuss what kind of theories can describe the physics near the critical point by requiring the matching of topological field theories in the infrared. As one of the possibilities, we propose a scenario where the $rho$ and $omega$ mesons form a $U(N_f)$ gauge theory near the critical point. In the phase where the chiral symmetry is restored, they become the dual gauge boson of the gluon related by the level-rank duality between the three dimensional gauge theories, $SU(N)_{N_f}$ and $U(N_f)_{-N}$.
We are aiming to construct Quark Hadron Physics and Confinement Physics based on QCD. Using SU(3)$_c$ lattice QCD, we are investigating the three-quark potential at T=0 and $T e 0$, mass spectra of positive and negative-parity baryons in the octet and the decuplet representations of the SU(3) flavor, glueball properties at T=0 and $T e 0$. We study also Confinement Physics using lattice QCD. In the maximally abelian (MA) gauge, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to a large effective off-diagonal gluon mass, $M_{rm off} simeq 1.2 {rm GeV}$. Due to the large off-diagonal gluon mass in the MA gauge, infrared QCD is abelianized like nonabelian Higgs theories. In the MA gauge, there appears a macroscopic network of the monopole world-line covering the whole system. From the monopole current, we extract the dual gluon field $B_mu$, and examine the longitudinal magnetic screening. We obtain $m_B simeq$ 0.5 GeV in the infrared region, which indicates the dual Higgs mechanism by monopole condensation. From infrared abelian dominance and infrared monopole condensation, low-energy QCD in the MA gauge is described with the dual Ginzburg-Landau (DGL) theory.
In order to study the detailed dynamics and associated non-perturbative features of QCD, a dual version of the color gauge theory based on the topologically viable homogeneous fiber bundle approach has been analysed taking into account its magnetic symmetry structure. In the dynamically broken phase of magnetic symmetry, the associated flux tube structure on a S 2 -sphere in the magnetically condensed state of the dual QCD vacuum has been analyzed for the profiles of the color electric field using flux quantization and stability conditions. The color electric field has its intimate association with the vector mode of the magnetically condensed QCD vacuum and such field configurations have been analyzed to show that the color electric flux gets localized towards the poles for a large sphere case while it gets uniformly distributed for the small sphere case in the infrared sector of QCD. The critical flux tube densities have been computed for various couplings and are shown to be in agreement with that for lead-ion central collisions in the near infrared sector of QCD. The possible annihilation/unification of flux tubes under some typical flux tube density and temperature conditions in the magnetic symmetry broken phase of QCD has also been analyzed and shown to play an important role in the process of QGP formation. The thermal variation of the profiles of the color electic field is further investigated which indicates the survival of flux tubes even in the thermal domain that leads the possibility of the formation of some exotic states like QGP in the intermedate regime during the quark-hadron phase transition.
I review applications of superconformal algebra. light-front holography, and an extended form of conformal symmetry to hadron spectroscopy and dynamics. QCD is not supersymmetrical in the traditional sense -- the QCD Lagrangian is based on quark and gluonic fields -- not squarks nor gluinos. However, its hadronic eigensolutions conform to a representation of superconformal algebra. and provide a unified Regge spectroscopy of meson, baryon, and tetraquarks with a universal Regge slope. The pion $q bar q$ eigenstate is composite but yet has zero mass for $m_q=0.$ Light-Front Holography also predicts the form of the nonperturbative QCD running coupling in agreement with the effective charge determined from measurements of the Bjorken sum rule. One also obtains viable predictions for hadron dynamics such as spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. The combined approach of light-front holography and superconformal algebra also provides insight into the origin of the QCD mass scale and color confinement. A key tool is the dAFF principle which shows how a mass scale can appear in the Hamiltonian and the equations of motion while retaining the conformal symmetry of the action. When one applies the dAFF procedure to chiral QCD, a mass scale $kappa$ appears which determines the hadron masses in the absence of the Higgs coupling. The result is an extended conformal symmetry which has a conformally invariant action even though an underlying mass scale appears in the Hamiltonian. Although conformal symmetry is strongly broken by the heavy quark mass, the supersymmetric mechanism, which transforms mesons to baryons (and baryons to tetraquarks), still holds and gives remarkable mass degeneracies across the spectrum of light, heavy-light and double-heavy hadrons.
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