The hermitian Wilson-Dirac operator in smooth SU(2) instanton backgrounds

We study the spectral flow of the hermitian Wilson-Dirac operator \ham(m) as a function of $m$ in smooth SU(2) instanton backgrounds on the lattice. For a single instanton background with Dirichlet boundary conditions on \ham(m), we find a level crossing in the spectral flow of \ham(m), and we find the shape of the crossing mode at the crossing point to be in good agreement with the zero mode associated with the single instanton background. With anti-periodic boundary conditions on \ham(m), we find that the instanton background in the singular gauge has the correct spectral flow but the one in regular gauge does not. We also investigate the spectral flows of two instanton and instanton-anti-instanton backgrounds.Comment: 18 pages, Latex file, 12 postscript figure

Dual vortices in Abelian projected SU(2) in the Polyakov gauge

We study dual Abrikosov vortices in Abelian projected SU(2) gauge theory in the Polyakov gauge. We show that vortices are present in this gauge but they are suppressed with respect to the maximal Abelian gauge. We interpret this difference in terms of the shielding of the electric charge by the charged coset fields.Comment: Talk presented at LATTICE96(topology), 3 pages, latex, 4 eps figures, uses epsfig and espcrc2.sty (included

Relations Between Low-lying Quantum Wave Functions and Solutions of the Hamilton-Jacobi Equation

We discuss a new relation between the low lying Schroedinger wave function of a particle in a one-dimentional potential V and the solution of the corresponding Hamilton-Jacobi equation with -V as its potential. The function V is $\geq 0$, and can have several minina (V=0). We assume the problem to be characterized by a small anhamornicity parameter $g^{-1}$ and a much smaller quantum tunneling parameter $\epsilon$ between these different minima. Expanding either the wave function or its energy as a formal double power series in $g^{-1}$ and $\epsilon$, we show how the coefficients of $g^{-m}\epsilon^n$ in such an expansion can be expressed in terms of definite integrals, with leading order term determined by the classical solution of the Hamilton-Jacobi equation. A detailed analysis is given for the particular example of quartic potential $V={1/2}g^2(x^2-a^2)^2$.Comment: LaTex, 48 pages, no figur

A New Approach to Flavor Symmetry and an Extended Naturalness Principle

A class of non-supersymmetric extensions of the Standard Model is proposed in which there is a multiplicity of light scalar doublets in a multiplet of a non-abelian family group with the Standard Model Higgs doublet. Anthropic tuning makes the latter light, and consequently the other scalar doublets remain light because of the family symmetry. The family symmetry greatly constrains the pattern of FCNC and proton decay operators coming from scalar-exchange. Such models show that useful constraints on model-building can come from an extended naturalness principle when the electroweak scale is anthropically tuned.Comment: 31 pages, 3 figure

Baryons in Holographic QCD

We study the baryon in holographic QCD with $D4/D8/\bar{D8}$ multi-$D$ brane system. In holographic QCD, the baryon appears as a topologically non-trivial chiral soliton in a four-dimensional effective theory of mesons. We call this topological soliton as Brane-induced Skyrmion. Some review of $D4/D8/\bar{D8}$ holographic QCD is presented from the viewpoints of recent hadron physics and phenomenologies. Four-dimensional effective theory with pions and $\rho$ mesons is uniquely derived from the non-abelian Dirac-Born-Infeld (DBI) action of $D8$ brane with $D4$ supergravity background, without small amplitude expansion of meson fields to discuss chiral solitons. For the hedgehog configuration of pion and $\rho$-meson fields, we derive the energy functional and the Euler-Lagrange equation of Brane-induced Skyrmion from the meson effective action induced by holographic QCD. Performing the numerical calculation, we obtain the pion profile $F(r)$ and the $\rho$-meson profile $G(r)$ of the Brane-induced Skyrmion, and estimate its total energy, energy density distribution, and root-mean-square radius. These results are compared with the experimental quantities of baryons and also with the profiles of standard Skyrmion without $\rho$ mesons. We analyze interaction terms of pions and $\rho$ mesons in Brane-induced Skyrmion, and consider the role of $\rho$-meson component appearing in baryons.Comment: 28 pages, 11 figure

Anomalous gauge couplings of the Higgs boson at high energy photon colliders

We study the sensitivity of testing the anomalous gauge couplings $g_{HVV}$'s of the Higgs boson in the formulation of linearly realized gauge symmetry via the processes $\gamma\gamma\to ZZ$ and $\gamma\gamma\to WWWW$ at polarized and unpolarized photon colliders based on $e^+e^-$ linear colliders of c.m.~energies 500 GeV, 1 TeV, and 3 TeV. Signals beyond the standard model (SM) and SM backgrounds are carefully studied. We propose certain kinematic cuts to suppress the standard model backgrounds. For an integrated luminosity of 1 ab$^{-1}$, we show that (a) $\gamma\gamma\to ZZ$ can provide a test of $g_{H\gamma\gamma}$ to the $3\sigma$ sensitivity of $O(10^{-3}-10^{-2})$ TeV$^{-1}$ at a 500 GeV ILC, and $O(10^{-3})$ TeV$^{-1}$ at a 1 TeV ILC and a 3 TeV CLIC, and (b) $\gamma\gamma\to WWWW$ at a 3 TeV CLIC can test all the anomalous couplings $g_{HVV}$'s to the $3\sigma$ sensitivity of $O(10^{-3}-10^{-2})$ TeV$^{-1}$.Comment: 30 pages, 17 figure

Introduction to light cone field theory and high energy scattering

In this set of four lectures, we provide an elementary introduction to light cone field theory and some of its applications in high energy scattering.Comment: 28 pages, LaTeX, invited lectures at Cape Town summer school in theoretical physic

Does quantum mechanics tell an atomistic spacetime?

The canonical answer to the question posed is "Yes." -- tacitly assuming that quantum theory and the concept of spacetime are to be unified by `quantizing' a theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics arise as a coarse-grained reflection of the atomistic nature of spacetime? -- We speculate that this may indeed be the case. We recall the similarity between evolution of classical and quantum mechanical ensembles, according to Liouville and von Neumann equation, respectively. The classical and quantum mechanical equations are indistinguishable for objects which are free or subject to spatially constant but possibly time dependent, or harmonic forces, if represented appropriately. This result suggests a way to incorporate anharmonic interactions, including fluctuations which are tentatively related to the underlying discreteness of spacetime. Being linear and local at the quantum mechanical level, the model offers a decoherence and natural localization mechanism. However, the relation to primordial deterministic degrees of freedom is nonlocal.Comment: Based on invited talks at Fourth International Workshop DICE2008, held at Castello Pasquini / Castiglioncello, Italy, 22-26 September 2008 and at DISCRETE'08 - Symposium on Prospects in the Physics of Discrete Symmetries, held at IFIC, Valencia, Spain, 11-16 December 2008 - to appear in respective volumes of Journal of Physics: Conference Serie

Brane-induced Skyrmion on S^3: baryonic matter in holographic QCD

We study baryonic matter in holographic QCD with D4/D8/\bar{D8} multi-D brane system in type IIA superstring theory. The baryon is described as the "brane-induced Skyrmion", which is a topologically non-trivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the "truncated-resonance model" approach for the baryon analysis, including pion and \rho meson fields below the ultraviolet cutoff scale M_KK \sim 1GeV, to keep the holographic duality with QCD. We describe the baryonic matter in large N_c as single brane-induced Skyrmion on the three-dimensional closed manifold S^3 with finite radius R. The interactions between baryons are simulated by the curvature of the closed manifold S^3, and the decrease of the size of S^3 represents the increase of the total baryon-number density in the medium in this modeling. We investigate the energy density, the field configuration, the mass and the root-mean-square radius of single baryon on S^3 as the function of its radius R. We find a new picture of "pion dominance" near the critical density in the baryonic matter, where all the (axial) vector meson fields disappear and only the pion field survive. We also find the "swelling" phenomena of the baryons as the precursor of the deconfinement, and propose the mechanism of the swelling in general context of QCD. The properties of the deconfinement and the chiral symmetry restoration in the baryonic matter are examined by taking the proper order parameters. We also compare our truncated-resonance model with another "instanton" description of the baryon in holographic QCD, considering the role of cutoff scale M_KK.Comment: 25 pages, 12 figure

General massive gauge theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is used to construct massive gauge theories. We consider the interactions of $r$ massive and $s$ massless gauge fields together with $(r+s)$ fermionic ghost and anti-ghost fields. First order gauge invariance requires the introduction of unphysical scalars (Goldstone bosons) and fixes their trilinear couplings. At second order additional physical scalars (Higgs fields) are necessary, their coupling is further restricted at third order. In case of one physical scalar all couplings are determined by gauge invariance, including the Higgs potential. For three massive and one massless gauge field the $SU(2)\times U(1)$ electroweak theory comes out as the unique solution.Comment: 20 pages, latex, no figure