Solitons in the false vacuum
When a potential for a scalar field has two local minima, there arises structure of spherical shells due to gravitational interactions.
hep-th↗
arXiv subjects
Yutaka Hosotani
Publications and source records attributed to Yutaka Hosotani.
Monopoles and Dyons in the Pure Einstein-Yang-Mills Theory
In the pure Einstein-Yang-Mills theory in four dimensions there exist monopole and dyon solutions. The spectrum of the solutions is discrete in asymptotically flat or de Sitter space, whereas it is continuous in asymptotically anti-de Sitter space. The solutions are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. In asymptotically anti-de Sitter space a class of monopole solutions have no node in non-Abelian magnetic fields, and are stable against spherically symmetric perturbations.
gr-qc↗
Stable monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter Space
A continuum of new monopole and dyon solutions in the Einstein-Yang-Mills theory in asymptotically anti-de Sitter space are found. They are regular everywhere and specified with their mass, and non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields are shown to be stable against spherically symmetric linear perturbations.
gr-qc↗
Monople and dyon solutions in the Einstein Yang-Mills theory in asymptotically AdS space
Regular monopole and dyon solutions to the SU(2) Einstein Yang-Mills equations in asymptotically anti-de Sitter space are discussed. A class of monopole solutions are shown to be stable against spherically symmetric linear perturbations.
gr-qc↗
The Hamilton-Jacobi Equations for Strings and p-Branes
Simple derivation of the Hamilton-Jacobi equation for bosonic strings and p-branes is given. The motion of classical strings and p-branes is described by two and p+1 local fields, respectively. A variety of local field equations which reduce to the Hamilton-Jacobi equation in the classical limit are given. They are essentially nonlinear, having no linear term.
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Complex Monopoles in the Georgi-Glashow-Chern-Simons Model
We investigate the three dimensional Georgi-Glashow model with a Chern-Simons term. We find that there exist complex monopole solutions of finite action. They dominate the path integral and disorder the Higgs vacuum, but electric charges are not confined. Subtleties in the gauge fixing procedure in the path integral and issues related to Gribov copies are noted.
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Antiferromagnetic S=1/2 Heisenberg Chain and the Two-flavor Massless Schwinger Model
An antiferromagnetic S=1/2 Heisenberg chain is mapped to the two-flavor massless Schwinger model at θ=π. The electromagnetic coupling constant and velocity of light in the Schwinger model are determined in terms of the Heisenberg coupling and lattice spacing in the spin chain system.
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Gauge Theory Description of Spin Ladders
A s=1/2 antiferromagnetic spin chain is equivalent to the two-flavor massless Schwinger model in an uniform background charge density in the strong coupling. The gapless mode of the spin chain is represented by a massless boson of the Schwinger model. In a two-leg spin ladder system the massless boson aquires a finite mass due to inter-chain interactions. The gap energy is found to be about .25 k |J'| when the inter-chain Heisenberg coupling J' is small compared with the intra-chain Heisenberg coupling. k is a constant of O(1). It is also shown that a cyclically symmetric N-leg ladder system is gapless or gapful for an odd or even N, respectively.
cond-mat.stat-mech↗
Complex Monopoles in YM + Chern-Simons Theory in 3 Dimensions
In this talk, we give a brief discussion of complex monopole solutions in the three dimensional Georgi-Glashow model with a Chern-Simons term. We find that there exist complex monopole solutions of finite action. They dominate the path integral and disorder the Higgs vacuum, but electric charges are not confined. Subtleties in the model and issues related to Gribov copies are also noted.
hep-th↗
Bosonized Massive N-flavor Schwinger Model
The massive N-flavor Schwinger model is analyzed by the bosonization method. The problem is reduced to the quantum mechanics of N degrees of freedom in which the potential needs to be self-consistently determined by its ground-state wave function and spectrum with given values of the $θ$ parameter, fermion masses, and temperature. Boson masses and fermion chiral condensates are evaluated. In the N=1 model the anomalous behavior is found at $θ\sim π$ and $m/μ\sim 0.4$. In the N=3 model an asymmetry in fermion masses $(m_1 < m_2 \ll m_3)$ removes the singularity at $θ=π$ and T=0. The chiral condensates at $θ=0$ are insensitive to the asymmetry in fermion masses, but are significantly sensitive at $θ=π$. The resultant picture is similar to that obtained in QCD by the chiral Lagrangian method.
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Gauge Theory Description of Spin Chains and Ladders
An S=1/2 anti-ferromagnetic spin chain is mapped to the two-flavor massless Schwinger model, which admits a gapless mode. In a spin ladder system rung interactions break the chiral invariance. These systems are solved by bosonization. If the number of legs in a cyclically symmetric ladder system is even, all of the gapless modes of spin chains become gapful. However, if the number of legs is odd, one combination of the gapless modes remains gapless. For a two-leg system we find that the spin gap is about .36 |J'| when the inter-chain Heisenberg coupling J' is small compared with the intra-chain Heisenberg coupling.
cond-mat.stat-mech↗
Maxwell-Chern-Simons Scalar Electrodynamics at Two Loop
The Maxwell-Chern-Simons gauge theory with charged scalar fields is analyzed at two loop level. The effective potential for the scalar fields is derived in the closed form, and studied both analytically and numerically. It is shown that the U(1) symmetry is spontaneously broken in the massless scalar theory. Dimensional transmutation takes place in the Coleman-Weinberg limit in which the Maxwell term vanishes. We point out the subtlety in defining the pure Chern-Simons scalar electrodynamics and show that the Coleman-Weinberg limit must be taken after renormalization. Renormalization group analysis of the effective potential is also given at two loop.
hep-th↗
Chiral Dynamics in Weak, Intermediate, and Strong Coupling QED in Two Dimensions
N flavor QED in two dimensions is reduced to a quantum mechanics problem with N degrees of freedom for which the potential is determined by the ground state of the problem itself. The chiral condensate is determined at all values of temperature, fermion masses, and the $θ$ parameter. In the single flavor case, the anomalous mass (m) dependence of the chiral condensate at $θ=π$ at low temperature is found. The critical value is given by $m_c \sim .437 e/\sqrtπ$.
hep-th↗
Anomalous Behavior in the Massive Schwinger Model
We evaluate the chiral condensate and Polyakov loop in two-dimensional QED with a fermion of an arbitrary mass ($m$). We find discontinuous $m$ dependence in the chiral condensate and anomalous temperature dependence in Polyakov loops when the vacuum angle $θ$$\sim$$π$ and $m$=O($e$). These nonperturbative phenomena are due to the bifurcation process in the solutions to the vacuum eigenvalue equation.
hep-th↗
Spontaneous Symmetry Breaking at Two Loop in 3-d Massless Scalar Electrodynamics
In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics with $ ϕ^6$ coupling, the $U(1)$ symmetry is spontaneously broken at two loop order regardless of the presence or absence of the Maxwell term. Dimensional transmutation takes place in pure Chern-Simons scalar electrodynamics. The beta function for the $ϕ^6$ coupling is independent of gauge couplings.
hep-th↗
Gauge Theory Model -- quark dynamics and anti-ferromagnets
Two-dimensional QED with N-flavor fermions serves as a model of quark dynamics in QCD as well as an effective theory of an anti-ferromagnetic spin chain. It is reduced to N-degree quantum mechanics in which a potential is self-consistently determined by the Schrödinger equation itself.
hep-th↗
Confinement and chiral condensates in 2-d QED with massive N-flavor fermions
We evaluate Polyakov loops and string tension in two-dimensional QED with both massless and massive $N$-flavor fermions at zero and finite temperature. External charges, or external electric fields, induce phases in fermion masses and shift the value of the vacuum angle parameter $θ$, which in turn alters the chiral condensate. In particular, in the presence of two sources of opposite charges, $q$ and $-q$, the shift in $θ$ is $2π(q/e)$ independent of $N$. The string tension has a cusp singularity at $θ=\pmπ$ for $N\ge 2$ and is proportional to $m^{2N/(N+1)}$ at $T=0$.
hep-th↗
Spontaneous Breakdown of the Lorentz Invariance in Three-Dimensional Gauge Theories
In a class of renormalizable three-dimensional abelian gauge theory the Lorentz invariance is spontaneously broken by dynamical generation of a magnetic field $B$. The true ground state resembles that of the quantum Hall effect. An originally topologically massive photon becomes gapless, fulfilling the role of the Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance. We give a simple explanation and a sufficient condition for the spontaneous breaking of the Lorentz invariance with the aid of the Nambu-Goldstone theorem. The decrease of the energy density by $B \not= 0$ is understood mostly due to the shift in zero-point energy of photons. For PASCOS'94.
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