Dynamical symmetry breaking in the SU (2) gauge theory

Properties of vacua of the SU(2) gauge theory containing massless and massive fermions are investigated within the one-loop approximation. As a result of a condensation of composite scalar made of gauge fields, some gauge fields acquire a mass and the original SU(2) gauge symmetry is suggested to breake down to U (1). We evaluate the effective potential for the constant magnetic field and then extract the so-called dielectric permeability κ from it. The phase is called paramagnetism for positive κ, perfect paramagnetism for vanishing κ and ferromagnetism for negative κ. The choice of a favorable phase is determined by the value of the coupling constant and the number and the mass of fermions. The perfect paramagnetic phase is most precisely studied. It is shown that solitons with non-zero charges carry divergent energies. Then, the electric flux around the charge is shown to be squeezed into a string in that phase.     

Coleman-Weinberg symmetry breaking in the chiral SU(n) × SU(n) linear σ model

The onset of symmetry breaking in the chiral SU(n) × SU(n) linear σ model is investigated. It is shown that the model possesses no stable fixed points in d = 4 ? ? dimensions and that the chiral symmetry of the theory can be broken via the CW mechanism when d = 4. The implications of these results are discussed.     

Patterns of symmetry breaking in supersymmetric gauge theories

We give a group-theoretical analysis of the spontaneous breaking of the gauge group in supersymmetric Yang-Mills theories with unbroken supersymmetry.     

Translation symmetry breaking in four dimensional lattice gauge theories

We consider lattice gauge theories with finite abelian groupG in the weak coupling regime. It is shown that there is only one translation invariant equilibrium state for the infinite system. In four dimensions we construct a nontranslation invariant equilibrium state, describing an infinite system with localized magnetic flux tube, starting and ending at infinity.     

On the character of scalar symmetry breaking in gauge theories

It is shown that the phenomenon of spontaneous breaking of an approximate scale symmetry in gauge theories and the PCAC dynamics are incompatible.     

Dynamical symmetry breaking in SYM theories as a non-semiclassical effect

We study supersymmetry breaking effects in N=1 SYM from the point of view of quantum effective actions. Restrictions on the geometry of the effective potential from superspace are known to be problematic in quantum effective actions, where explicit supersymmetry breaking can and must be studied. On the other hand the true ground state can be determined from this effective action, only. We study the problem whether some parts of superspace geometry are still relevant for the effective potential and discuss whether the ground states found this way justify a low energy approximation based on this geometry. The answer to both questions is negative. Essentially non-semiclassical effects change the behavior of the auxiliary fields completely and lead to the demand of a new interpretation of superspace geometry. These non-semiclassical effects can break supersymmetry. Received: 10 January 2002 / Revised version: 13 April 2002 / Published online: 18 October 2002 RID="*" ID="*" Work supported in part by the Schweizerischer Nationalfonds RID="a" ID="a" e-mail: bergamin@tph.tuwien.ac.at     

The C-theorem and chiral symmetry breaking in asymptotically free vectorlike gauge theories

We confront Cardy's suggested c-function for four-dimensional field theories with the spontaneous breaking of chiral symmetries in asymptotically free vectorlike gauge theories with fermions transforming according to different representations under the gauge group. Assuming that the infrared limit of the c-function is determined by the dimension of the associated Goldstone manifold, we find that this c-function always decreases between the ultraviolet and infrared fixed points.     

The many-body content of quantum gauge theories and spontaneous symmetry breaking

The many-body content of quantum field theories is studied by performing the limit velocity of light → ∞. It is found that the limit of the Goldstone model is the Bogoliubov model of superfluidity, and the limit of the vacuum of spontaneously broken abelian theories is a plasma whose excitations are the limit of the massive gauge bosons. The method appears suitable to study dynamical supersymmetry breaking and colour confinement.     

Dynamical supersymmetry breaking in two-dimensional N = 1 supergravity theories

We investigate a possible dynamical mechanism for spontaneous supersymmetrybreaking in N = 1 supergravity theories in 1 + 1 space-time dimensions. It will be shown that supersymmetry is never broken at the tree level, but it can be broken for a certain class of models by quantum effects due to trace anomalies of the energy-momentum tensor and the supercurrent.     

Spontaneous chiral symmetry breaking for a U(N) gauge theory on a lattice

We study the breakdown of chiral invariance by calculating, in the infinite coupling, large-N limit, the generating functional of a U(N) gauge theory with one fermion, expressed on a lattice with the naive, chiral symmetric action. We compute the link integral over the gauge fields and the expression obtained after the integration over the fermions is recast under the form of a generating functional for bosonic fields. Then, a saddle-point method allows the calculation of the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ for which a non-zero value signals the spontaneous breakdown of chiral symmetry. The analysis of the fluctuations around the saddle point allows one to exhibit the Goldstone modes corresponding to those global symmetries of the fermionic lattice action which are simultaneously broken.