On mass matrices in extended technicolor theories

General properties of mass matrices in extended technicolor models are investigated. The question of hermitean quark mass matrices in both charge sectors is addressed. A new class of models using non-conjugate, inequivalent representations is also considered. Mass matrices in such models need not have specific symmetry properties. Only one model in this class is asymptotically free.     

Obtaining Mw = Mz cos θ in technicolor theories

We show that the successful relation M_w = M_z cos θ is preserved in the technicolor formulation of the dynamical Higgs mechanism provided only that the creation operators for Goldstone bosons associated with broken generators belong to the $\text{I}{}_{\mathrm{<mtext>w</mtext>}}\text{=}\text{1}\text{2}$ representation of the weak isospin group. We present a plausibility argument that this is indeed the case. No additional isospin or isospin-like global SU(2) symmetries are then required allowing isospin to be spontaneously broken. This may be of help in producing a large $\text{m}{}_{\mathrm{<mtext>c</mtext>}}\text{m}{}_{\mathrm{<mtext>s</mtext>}}$ splitting. It is also shown how the weak hyperchange interaction can produce substantial vacuum isospin breaking in a theory which is only marginally asymptotically free. This mechanism predicts , providing a natural explanation for small neutrino masses.     

Subgroup alignment in hypercolor theories

To analyze the physical consequences of a dynamically broken theory of the weak interactions, we must know how the weak gauge group is aligned in an approximate flavor-symmetry group. For a large class of models, spectral-function sum rules enables us to determine this alignment explicitly. We work out the pattern of the electroweak symmetry breakdown for several sample models. Critical values of weak mixing angles are found at which the breakdown pattern changes discontinously. We compute pseudo-Goldstone boson masses, and find that some models contain unusually light charged or colored pseudo-Goldstone bosons.     

Monopole vacuum in non-Abelian theories

It is shown that, in the theory of interacting Yang-Mills fields and a Higgs field, there is a topological degeneracy of Bogomol'nyi-Prasad-Sommerfield (BPS) monopoles and that there arises, in this case, a chromoelectric monopole characterized by a new topological variable that describes transitions between topological states of the monopole in Minkowski space (in just the same way as an instanton describes such transitions in Euclidean space). The limit of an infinitely large mass of the Higgs field at a finite density of the Bogomol'nyi-Prasad-Sommerfield monopole is considered as a model of the stable vacuum in pure Yang-Mills theory. It is shown that, in QCD, such a monopole vacuum may lead to a growing potential, a topological confinement, and an additional mass of the η₀ meson. The relationship between the result obtained here for the generating functional of perturbation theory and the Faddeev-Popov integral is discussed.     

Vacuum alignment in supersymmetric gauge theories

The vacuum alignment problem is analyzed in the context of supersymmetric gauge theories with dynamical symmetry breaking. Three cases are distinguished, depending on whether the vacuum expectation value of the weak gauge current superfield in vacuum characterized by the orientation Ω is zero for all Ω, for some Ω, or for no Ω. In the first case, a non-renormalization theorem is proved to all orders in the weak coupling, showing that the usual criterion of minimizing the vacuum energy density is insufficient to determine the alignment, and possible resolutions of the problem are discussed. The second case is similar, except that the possible alignments are resricted to the range of Ω giving a vanishing VEV and the weak gauge group may then be broken non-minimally. In the third case, supersymmetry is itself broken at the tree level by the weak interactions. The supersymmetric generalization of the Schwinger mechanism for dynamical mass generation is described.     

Reconstruction of dynamics from the vacuum in lattice theories

The Coester-Haag scheme to define the dynamics from the vacuum is applied to lattice theories. As an example the reconstruction algorithm is carried out for two trial ground states. The reconstruction approach may by itself define the theory or, when coupled with a variational calculation and a fixed external Hamiltonian, it provides a method to find the proximity of the trial ground states to actual states of the theory. This technique is applied to the reconstruction examples in the continuum limit.     

On the problem of vacuum energy in brane theories

We point out that modern brane theories suffer from a severe vacuum energy problem. To be specific, the Casimir energy associated with the matter fields confined to the brane, is stemming from the one and the same localization mechanism which forms the brane itself, and is thus generically unavoidable. Possible practical solutions are discussed, including in particular spontaneously broken supersymmetry, and quantum mechanically induced brane tension.     

On the instability of the vacuum in multidimensional scalar theories

The one-loop effective potential in a scalar theory with quartic interaction on the spaceM ⁴×T ⁿ forn=2 is calculated and is shown to be unbounded from below. This is an indication of a possible instability of the vacuum of theλψ ⁴ model onM ⁴, when it is regarded as a low-energy sector of the theory obtained by dimensional reduction of the original six-dimensional one. It is argued that, in some range of the values of the parameters of the theory, higher-loop corrections do not change this result qualitatively. The issue of stability for other values of the numbern of extra dimensions is also discussed.     

Calculation of the regularized vacuum energy in cavity field theories

A novel technique based on Schwinger's proper time method is applied to the Casimir problem of the M.I.T. bag model. Calculations of the regularized vacuum energies of massless scalar and Dirac spinor fields confined to a static and spherical cavity are presented in a consistent manner. While our results agree partly with previous calculations based on asymptotic methods, the main advantage of our technique is that the numerical errors are under control. Interpreting the bag constant as a vacuum expectation value, we investigate potential cancellations of boundary divergences between the canonical energy and its bag constant counterpart in the fermionic case. It is found that such cancellations do not occur. Received: 19 March 1999 / Published online: 28 September 1999     

Correlation length of the vacuum condensate in lattice gauge theories

The correlation length λ of the vacuum condensateG ₂ is determined by Montecarlo simulation of anSU(2) lattice gauge theory. The result isG ₂ λ⁴ = 0.0019 ± 0.0002. The implications of this result are discussed.     

Quasi-periodic boundary conditions and the vacuum structure in gauge theories

The role of the θ angle occuring in the vacuum structure of gauge theories is illustrated by means of a quantum mechanical example.     

Perturbative vacuum wavefunctional for gauge theories in the Milne space

The spectrum of vacuum fluctuations in the Milne space (i.e. the τ−η$\tau -\eta$ coordinate system) is an important ingredient in the thermalization studies in relativistic heavy ion collisions. In this paper, the Schrödinger functional for the gauge theory perturbative vacuum is derived for the Milne space. The Wigner-transform of the corresponding vacuum density functional is also found together with the propagators. We finally identify the fluctuation spectrum in vacuum, and show the equivalence between the present approach and the symplectic product based method (Dusling et al., 2011; Epelbaum and Gelis, 2013).     

Monopole classical solutions and the vacuum structure in lattice gauge theories

Classical solutions corresponding to monopole-antimonopole pairs are found in 3d and 4d SU(2) and U(1) lattice gauge theories. The stability of these solutions in various theories is studied.