Yutaka Hosotani

Dynamics of non-integrable phases and gauge symmetry breaking

On a multiply-connected space the non-integrable phase factor/ital P/ exp(ig..integral../ital A//sub ..mu..//ital dx//sup ..mu..//r brace/), a path-ordered line integral along anon-contractable loop, becomes a dynamical degree of freedom in gauge theory.The dynamics of such non-integrable phases are examined in detail with themost general boundary condition for gauge fields and fermions. Sometimesthe dynamics of the non-integrable phases compensate the arbitrariness inthe boundary condition imposed, leading to the same physics results. Inother cases the dynamics of the non-integrable phases induce spontaneousbreaking of non-Abelian gauge symmetry. In other words the physically realizedsymmetry of the system differs from, and can be either greater or smaller than,the symmetry of the boundary condition. The effective potential for thenon-integrable phases in the /ital SU/(/ital N/) gauge theory on/ital S//sup 1//direct product//ital R//sup 1/ital d//minus/2/is computed in the one-loop approximation. It is shown that the gauge symmetryis dynamically broken in the presence of fermions in the adjoint representation,depending on the value of the boundary condition parameter./copyright/ 1989 Academic Press, Inc.

Monopoles, dyons and black holes in the four-dimensional Einstein-Yang-Mills theory

A continuum of monopole, dyon, and black hole solutions exists in the Einstein-Yang-Mills theory in asymptotically anti\char21{}de Sitter space. Their structure is studied in detail. The solutions are classified by non-Abelian electric and magnetic charges and the Arnowitt-Deser-Misner mass. The stability of the solutions which have no node in non-Abelian magnetic fields is established. There exist critical spacetime solutions which terminate at a finite radius, and have universal behavior. The moduli space of the solutions exhibits a fractal structure as the cosmological constant approaches zero.

Spontaneously broken Lorentz invariance in three-dimensional gauge theories☆

Abstract In a wide class of three-dimensional Abelian gauge theories with a bare Chern-Simons term, the Lorentz invariance is spontaneously broken by dynamical generation of a nonvanishing magnetic field. The originally massive photon becomes massless, fulfilling the role of a Nambu-Goldstone boson associated with the spontaneous breaking of the Lorentz invariance.

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 by their mass and their non-Abelian electric and magnetic charges. A class of monopole solutions which have no node in non-Abelian magnetic fields is shown to be stable against spherically symmetric linear perturbations.

The massive multi-flavor Schwinger model

Abstract QED with N species of massive fermions on a circle of circumference L is analyzed by bosonization. The problem is reduced to the quantum mechanics of the 2 N fermionic and one gauge field zero modes on the circle, with nontrivial interactions induced by the chiral anomaly and fermions masses. The solution is given for N = 2 and fermion masses ( m ) much smaller than the mass of the U (1) boson with mass μ = 2e 2 π when all fermions satisfy the same boundary conditions. We show that the two limits m → 0 and L → ∞ fail to commute and that the behavior of the theory critically depends on the value of mL| cos 1 2 θ| where θ is the vacuum angle parameter. When the volume is large μL ⪢ 1, fermion condensate 〈 ψ ψ〉 is −(e 4γ mμ 2 cos 4 1 2 θ/4π 3 ) 1 3 or respectively. Its correlation function decays algebraically with a critical exponent η = 1 when m cos 1 2 θ = 0 .

Spontaneous breakdown of Lorentz invariance

We reexamine three-dimensional gauge theory with a Chern-Simons term in which Lorentz invariance is spontaneously broken by the dynamical generation of a magnetic field. A nonvanishing magnetic field leads, through the Nambu-Goldstone theorem, to a decrease in the zero-point energies of photons, which accounts for a major part of the mechanism. The asymmetric spectral flow plays an important role. The instability in pure Chern-Simons theory is also noted.

Spontaneous symmetry breaking at two loop in 3-D massless scalar electrodynamics

Abstract 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.

Spontaneous magnetization in Lorentz invariant theories

Abstract In a class of three-dimensional Abelian gauge theories with both light and heavy fermions, heavy chiral fermions can trigger dynamical generation of a magnetic field, leading to the spontaneous breaking of the Lorentz invariance. Finite masses of light fermions tend to restore the Lorentz invariance.

Symmetry breaking by Wilson lines and finite-temperature effects☆

Abstract In this paper we study gauge symmetry breaking and restoration in an SU( N ) gauge theory defined on space-time manifold R 1, d −2 × S 1 when fermions obey non-trivial boundary conditions. We derive the one-loop effective potentials for the non-integrable phases of Wilson lines at both zero and finite temperature, using the zeta-function technique. It is shown that gauge symmetry can be broken with fermions in the adjoint representation, but is restored at high temperature. Detailed analyses are given for the groups SU(2), SU(3) and SU(5) on R 1,2 × S 1 .

Maxwell-Chern-Simons scalar electrodynamics at two loops

Abstract 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 loops.