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Register a new userHidden local symmetry and color confinement
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Ryuichiro Kitano
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The hidden local symmetry is a successful model to describe the properties of the vector mesons in QCD. We point out that if we identify this hidden gauge theory as the magnetic picture of QCD, a linearized version of the model simultaneously describes color confinement and chiral symmetry breaking. We demonstrate that such a structure can be seen in the Seiberg dual picture of a softly broken supersymmetric QCD. The model possesses exact chiral symmetry and reduces to QCD when mass parameters are taken to be large. Working in the regime of the small mass parameters, we show that there is a vacuum where chiral symmetry is spontaneously broken and simultaneously the magnetic gauge group is Higgsed. If the vacuum we find persists in the limit of large mass parameters, one can identify the rho meson as the massive magnetic gauge boson, that is an essential ingredient for color confinement.
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We relate quark confinement, as measured by the Polyakov-loop order parameter, to color confinement, as described by the Kugo-Ojima/Gribov-Zwanziger scenario. We identify a simple criterion for quark confinement based on the IR behaviour of ghost and gluon propagators, and compute the order-parameter potential from the knowledge of Landau-gauge correlation functions with the aid of the functional RG. Our approach predicts the deconfinement transition in quenched QCD to be of first order for SU(3) and second order for SU(2) -- in agreement with general expectations. As an estimate for the critical temperature, we obtain T_c=284MeV for SU(3).
We propose a unified description of two important phenomena: color confinement in large-$N$ gauge theory, and Bose-Einstein condensation (BEC). We focus on the confinement/deconfinement transition characterized by the increase of the entropy from $N^0$ to $N^2$, which persists in the weak coupling region. Indistinguishability associated with the symmetry group -- SU($N$) or O($N$) in gauge theory, and S$_N$ permutations in the system of identical bosons -- is crucial for the formation of the condensed (confined) phase. We relate standard criteria, based on off-diagonal long range order (ODLRO) for BEC and the Polyakov loop for gauge theory. The constant offset of the distribution of the phases of the Polyakov loop corresponds to ODLRO, and gives the order parameter for the partially-(de)confined phase at finite coupling. We demonstrate this explicitly for several quantum mechanical systems (i.e., theories at small or zero spatial volume) at weak coupling, and argue that this mechanism extends to large volume and/or strong coupling. This viewpoint may have implications for confinement at finite $N$, and for quantum gravity via gauge/gravity duality.
Some aspects are discussed of the mechanism of color confinement in QCD by condensation of magnetic monopoles in the vacuum.
The color-flavor locking phenomenon in the magnetic picture can be the microscopic description of the quark confinement in QCD. We demonstrate it in an N=2 supersymmetric SU(Nc)xSU(Nc) quiver gauge theory coupled to Nf flavors of quarks (Nf<Nc). This model reduces to SU(Nc) gauge theory with Nf flavors when the vacuum expectations value of the link field is much larger than the dynamical scales, and thus provides a continuous deformation of the N=2 supersymmetric QCD. We study a vacuum which survives upon adding a superpotential term to reduce to N=1 while preserving the vectorial SU(Nf) flavor symmetry. We find a region of the parameter space where the confinement is described by the Higgsing of a weakly coupled magnetic SU(Nf)xU(1) gauge theory. The Higgsing locks the quantum numbers of SU(Nf) magnetic color to those of SU(Nf) flavor symmetry, and thus the massive magnetic gauge bosons become the singlet and adjoint representations of the flavor group, i.e, the vector mesons. If the qualitative picture remains valid in non-supersymmetric QCD, one can understand the Hidden Local Symmetry as the magnetic dual description of QCD, and the confining string is identified as the vortex of vector meson fields.
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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