Random matrix model at nonzero chemical potentials with anomaly effects

Phase diagram of the chiral random matrix model with U(1)A breaking term is studied with the quark chemical potentials varied independently at zero temperature, by taking the chiral and meson condensates as the order parameters. Although, without the U(1)A breaking term, chiral transition of each flavor can happen separately responding to its chemical potential, the U(1)A breaking terms mix the chiral condensates and correlate the phase transitions. In the three flavor case, we find that there are mixings between the meson and chiral condensates due to the U(1)A anomaly, which makes the meson condensed phase more stable. Increasing the hypercharge chemical potential ($\mu_Y$) with the isospin and quark chemical potentials ($\mu_I$, $\mu_q$) kept small, we observe that the kaon condensed phase becomes the ground state and at the larger $\mu_Y$ the pion condense phase appears unexpectedly, which is caused by the competition between the chiral restoration and the meson condensation. The similar happens when $\mu_Y$ and $\mu_I$ are exchanged, and the kaon condensed phase becomes the ground state at larger $\mu_I$ below the full chiral restoration.Comment: 12 pages, 8 figure

The back reaction and the effective Einstein's equation for the Universe with ideal fluid cosmological perturbations

We investigate the back reaction of cosmological perturbations on the evolution of the Universe using the renormalization group method. Starting from the second order perturbed Einstein's equation, we renormalize a scale factor of the Universe and derive the evolution equation for the effective scale factor which includes back reaction due to inhomogeneities of the Universe. The resulting equation has the same form as the standard Friedman-Robertson-Walker equation with the effective energy density and pressure which represent the back reaction effect.Comment: 16 pages, to appear in Phys. Rev.

Asymptotic Freedom: From Paradox to Paradigm

Asymptotic freedom was developed as a response to two paradoxes: the weirdness of quarks, and in particular their failure to radiate copiously when struck; and the coexistence of special relativity and quantum theory, despite the apparent singularity of quantum field theory. It resolved these paradoxes, and catalyzed the development of several modern paradigms: the hard reality of quarks and gluons, the origin of mass from energy, the simplicity of the early universe, and the power of symmetry as a guide to physical law.Comment: 26 pages, 10 figures. Lecture on receipt of the 2004 Nobel Prize. v2: typo (in Ohm's law) correcte

Back Reaction Problem in the Inflationary Universe

We investigate the back reaction of cosmological perturbations on an inflationary universe using the renormalization-group method. The second-order zero mode solution which appears by the nonlinearity of the Einstein equation is regarded as a secular term of a perturbative expansion, we renormalized a constant of integration contained in the background solution and absorbed the secular term to this constant in a gauge-invariant manner. The resultant renormalization-group equation describes the back reaction effect of inhomogeneity on the background universe. For scalar type classical perturbation, by solving the renormalization-group equation, we find that the back reaction of the long wavelength fluctuation works as a positive spatial curvature, and the short wavelength fluctuation works as a radiation fluid. For the long wavelength quantum fluctuation, the effect of back reaction is equivalent to a negative spatial curvature.Comment: 17 page

Abelianization of QCD in the Maximally Abelian Gauge and the Nambu-'t Hooft Picture for Color Confinement

We study the Nambu-'t Hooft picture for color confinement in terms of the abelianization of QCD and monopole condensation in the maximally abelian (MA) gauge. In the MA gauge in the Euclidean metric, the off-diagonal gluon amplitude is strongly suppressed, and then the off-diagonal gluon phase shows strong randomness, which leads to rapid reduction of the off-diagonal gluon correlation. In SU(2) and SU(3) lattice QCD in the MA gauge with the abelian Landau gauge, the Euclidean gluon propagator indicates a large effective mass of the off-diagonal gluon as $M_{\rm off} \simeq 1 {\rm GeV}$ in the intermediate distance as $0.2{\rm fm} \le r \le 0.8{\rm fm}$. Due to the infrared inactiveness of off-diagonal gluons, infrared QCD is well abelianized like nonabelian Higgs theories in the MA gauge. We investigate the inter-monopole potential and the dual gluon field $B_\mu$ in the MA gauge, and find longitudinal magnetic screening with $m_B \simeq$ 0.5 GeV in the infrared region, which indicates the dual Higgs mechanism by monopole condensation. We define the ``gluonic Higgs scalar field'' providing the MA projection, and find the correspondence between its hedgehog singularity and the monopole location in lattice QCD.Comment: Invited talk given at QCD02: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-9 Jul 200

Volume Expansion of Swiss-Cheese Universe

In order to investigate the effect of inhomogeneities on the volume expansion of the universe, we study modified Swiss-Cheese universe model. Since this model is an exact solution of Einstein equations, we can get an insight into non-linear dynamics of inhomogeneous universe from it. We find that inhomogeneities make the volume expansion slower than that of the background Einstein-de Sitter universe when those can be regarded as small fluctuations in the background universe. This result is consistent with the previous studies based on the second order perturbation analysis. On the other hand, if the inhomogeneities can not be treated as small perturbations, the volume expansion of the universe depends on the type of fluctuations. Although the volume expansion rate approaches to the background value asymptotically, the volume itself can be finally arbitrarily smaller than the background one and can be larger than that of the background but there is an upper bound on it.Comment: 22 pages, 7 figures, to be submitted to Phys. Rev.

The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number

A regularization for the baryon number consistent with the energy in the Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed with the regularized baryon number constrained to unity. It is furthermore demonstrated that this constraint prevents the soliton from collapsing when scalar fields are allowed to be space dependent. In this scheme the scalar fields actually vanish at the origin reflecting a partial restoration of chiral symmetry. Also the influence of this constraint on some static properties of baryons is discussed.Comment: 10 LaTeX pages 4 figures, report no UNITU-THEP-7/199

The Role of Monopoles for Color Confinement

We study the role of the monopole for color confinement by using the monopole current system. For the self-energy of the monopole current less than ln$(2d-1)$, long and complicated monopole world-lines appear and the Wilson loop obeys the area law, and therefore the monopole current system almost reproduces essential features of confinement properties in the long-distance physics. In the short-distance physics, however, the monopole-current theory would become nonlocal due to the monopole size effect. This monopole size would provide a critical scale of QCD in terms of the dual Higgs mechanism.Comment: 3 pages LaTeX, 3 figures, uses espcrc2.sty, Talk presented at lattice97, Edinburgh, Scotland, July. 199

Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges

We investigate in detail "instantaneous interquark potentials", interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous Q$\bar{\rm Q}$ potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2-3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the Q$\bar{\rm Q}$ case. $T$-length terminated Polyakov-line correlators and their corresponding "finite-time potentials" are also investigated in generalized Landau gauge