The structure of the gauge theory vacuum

The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.     

Skyrme Sphalerons of an O(3)-σ Model and the Calculation of Transition Rates at Finite Temperature

The reduced O(3)-σ model with an O(3)-σ→ O(2) symmetry breaking potential is considered with an additional Skyrmionic term, i.e. a totally antisymmetric quartic term in the field derivatives. This Skyrme term does not affect the classical static equations of motion which, however, allow an unstable sphaleron solution. Quantum fluctuations around the static classical solution are considered for the determination of the rate of thermally induced transitions between topologically distinct vacua mediated by the sphaleron. The main technical effect of the Skyrme term is to produce an extra measure factor in one of the flucuation path integrals which is therefore evaluated using a measuremodified Fourier-Matsubara decomposition (this being one of the few cases permitting this explicit calculation). The resulting transition rate is valid in a temperature region different from that of the original Skyrme-less model, and the crossover from transitions dominated by thermal fluctuations to those dominated by tunneling at the lower limit of this range depends on the strength of the Skyrme coupling.     

Soliton and vortex type solutions in non-linear chiral theories

Both static and time-dependent exact solutions of the classical field equations are presented for a chiral SU(2) × SU(2) non-linear pion Lagrangian. Of particular interest are the finite energy vortex-type solutions and the appearance of a topologically conserved charge. In two space-time dimensions, there are also genuine soliton solutions.     

Geometrical approach to stationary waves in a shallow grating

A geometrical analysis of the monochromatic solutions near the first band gap for a shallow Kerr grating is presented.The analysis is based on the coupled mode formalism and on Stokes variables. We investigate the electric field for nonzero energy flow, in particular we consider the phase difference between the counter-propagating coupled modes. Phase portraits for zero and nonzero energy flow are topologically different, and we clarify the way in which they are connected, thus identifying families of trajectories for nonzero flow that disappear when the flow goes to zero.     

Domain wall solutions with Abelian gauge fields

We study kink (domain wall) solutions in a model consisting of two complex scalar fields coupled to two independent Abelian gauge fields in a Lagrangian that has U(1)×U(1) gauge plus discrete symmetry. We find consistent solutions such that while the U(1) symmetries of the fields are preserved while in their respective vacua, they are broken on the domain wall. The gauge field solutions show that the domain wall is sandwiched between domains with constant magnetic fields.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.     

Positive energy in anti-de Sitter backgrounds and gauged extended supergravity

The energy functional of a field theory with anti-de Sitter background geometry can be positive for scalar potentials which are unbounded below and for vacua corresponding to critical points which are maxima or saddle points.     

Isovector solitons and Maxwell's equations

We present an isovector Lagrangian, which admits stable, nonsingular soliton solutions in three space dimensions. The spherical solution and its total energy are obtained via a variational procedure. An antisymmetric, second-rank tensor is defined in terms of the isovector field and its derivatives. This tensor satisfies Maxwell's equations. The corresponding current is identically conserved and the total charge is topologically quantized.     

Topological phase transition in anisotropic square-octagon lattice with spin–orbit coupling and exchange field

We investigate the topological phase transitions in an anisotropic square-octagon lattice in the presence of spin–orbit coupling and exchange field. On the basis of the Chern number and spin Chern number, we find a number of topologically distinct phases with tuning the exchange field, including time-reversal-symmetry-broken quantum spin Hall phases, quantum anomalous Hall phases and a topologically trivial phase. Particularly, we observe a coexistent state of both the quantum spin Hall effect and quantum anomalous Hall effect. Besides, by adjusting the exchange filed, we find the phase transition from time-reversal-symmetry-broken quantum spin Hall phase to spin-imbalanced and spin-polarized quantum anomalous Hall phases, providing an opportunity for quantum spin manipulation. The bulk band gap closes when topological phase transitions occur between different topological phases. Furthermore, the energy and spin spectra of the edge states corresponding to different topological phases are consistent with the topological characterization based on the Chern and spin Chern numbers.     

A class of time-machine solutions with a compact vacuum core

We present a class of curved-spacetime vacuum solutions which develop closed timelike curves at some particular moment. We then use these vacuum solutions to construct a time-machine model. The causality violation occurs inside an empty torus, which constitutes the time-machine core. The matter field surrounding this empty torus satisfies the weak, dominant, and strong energy conditions. The model is regular, asymptotically flat, and topologically trivial. Stability remains the main open question.     

Euclidean solutions and finite temperature gauge theory

It is shown that solutions of Euclidean gauge theory may have a direct physical interpretation at finite temperature. The existence of topologically distinct finite temperature solutions is proved.     

Cosmological constant from gauge fields on extra dimensions

We present a new model of dark energy which could explain the observed accelerated expansion of our Universe. We show that a five-dimensional Einstein–Yang–Mills theory defined in a flat Friedmann–Robertson–Walker universe compactified on a circle possesses degenerate vacua in four dimensions. The present Universe could be trapped in one of these degenerate vacua. With the natural requirement that the size of the extra dimension could be of the GUT scale or smaller, the energy density difference between the degenerate vacua and the true ground state can provide us with just the right amount of dark energy to account for the observed expansion rate of our Universe.     

Topology and Geometry of Smectic Order on Compact Curved Substrates

Smectic order on arbitrary curved substrate can be described by a differential form of rank one (1-form), whose geometric meaning is the differential of the local phase field of the density modulation. The exterior derivative of 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. We use the formalism of differential forms to systematically classify and characterize all low energy smectic states on torus as well as on sphere. A two dimensional smectic order confined on either manifold exhibits many topologically distinct low energy states. Different states are not accessible from each other by local fluctuations. The total number of low energy states scales as the square root of the system area. We also address the energetics of 2D smectic on a curved substrate and calculate the mean field phase diagram of smectic on a thin torus. Finally, we discuss the motion of disclinations for spherical smectics as low energy excitations, and illustrate the interesting connection between spherical smectic and the theory of elliptic functions.     

Coexistence of different vacua in the effective quantum field theory and multiple point principle

According to the Multiple Point Principle, our Universe is on the coexistence curve of two or more phases of the quantum vacuum. The coexistence of different quantum vacua can be regulated by the exchange of the global fermionic charges between the vacua, such as baryonic, leptonic, or family charge. If the coexistence is regulated by the baryonic charge, all the coexisting vacua exhibit the baryonic asymmetry. Due to the exchange of the baryonic charge between the vacuum and matter, which occurs above the electroweak transition, the baryonic asymmetry of the vacuum induces the baryonic asymmetry of matter in our Standard Model phase of the quantum vacuum. The present baryonic asymmetry of the Universe indicates that the characteristic energy scale, which regulates the equilibrium coexistence of different phases of quantum vacua, is about 10⁶ GeV.     

Exact Solutions to Pauli-Villars-Regulated Field Theories

We present a new class of quantum field theories which are exactly solvable. The theories are generated by introducing Pauli-Villars (PV) fermionic and bosonic fields with masses degenerate with the physical positive metric fields. An algorithm is given to compute the spectrum and corresponding eigensolutions. We also give the operator solution for a particular case and use it to illustrate some of the tenets of light-cone quantization. Since the solutions of the solvable theory contain ghost quanta, these theories are unphysical. However, the existence of an exact solution provides an important check on the implementation of PV-regulated discretized light-cone quantization (DLCQ). In the limit of exact mass degeneracy of the ghost and physical fields, the numerical DLCQ solutions are constrained to reduce to the explicit forms we give here. We also discuss how perturbation theory in the difference between the masses of the physical and PV particles could be developed, thus generating physical theories. The existence of explicit solutions of the solvable theory also allows one to study the relationship between the equal-time and light-cone vacua and eigensolutions.     

Topology of smectic order on compact substrates

Smectic orders on curved substrates can be described by differential forms of rank one (1-forms), whose geometric meaning is the differential of the local phase field of density modulation. The exterior derivative of the 1-form is the local dislocation density. Elastic deformations are described by superposition of exact differential forms. Applying this formalism to study smectic order on a torus as well as on a sphere, we find that both systems exhibit many topologically distinct low energy states that can be characterized by two integer topological charges. The total number of low energy states scales as the square root of the substrate area. For a smectic on a sphere, we also explore the motion of disclinations as possible low energy excitations, as well as its topological implications.     

Geometric realization of conformal field theory on Riemann surfaces

Conformal field theory on a family of Riemann surfaces is formulated. We derive equations of motion of vacua which are parametrized by moduli of Riemann surfaces and show that these vacua are characterized uniquely by these equations. Our theory has a deep connection with Sato's theory of KP equations.     

Effects of topology on the light front

We discuss how to construct theta vacua in the light-front field theories using the 1+1 dimensional Abelian Higgs model as an example. Unlike the non-gauged scalar field, zero modes of the Higgs field are in general dynamical as well as the gauge-field zero mode. While symmetry breaking is discussed in semi-classical treatment of the zero modes, the theta vacua are introduced in the quantum level by use of the large gauge symmetry.     

Dynamical instability of the vacuum in the lagrangian formalism of the Bethe-Salpeter bound states

By using the auxiliary field method, the stability problem of the vacua corresponding to the various solutions of the Schwinger-Dyson equation is discussed. The appearance of a tachyon bound state in the Bethe-Salpeter equation is shown to lead to the instability of the vacuum. This instability is resolved by the condensation into the tachyon mode which means the transition to another solution of the SD equation. The critical coupling of this instability is given explicitly.