Scalar lattice gauge theory

Scalar lattice gauge theories are models for scalar fields with local gauge symmetries. No fundamental gauge fields, or link variables in a lattice regularization, are introduced. The latter rather emerge as collective excitations composed from scalars. For suitable parameters scalar lattice gauge theories lead to confinement, with all continuum observables identical to usual lattice gauge theories. These models or their fermionic counterpart may be helpful for a realization of gauge theories by ultracold atoms. We conclude that the gauge bosons of the standard model of particle physics can arise as collective fields within models formulated for other “fundamental” degrees of freedom.     

Gauge symmetry as symmetry of matrix coordinates

We propose a new point of view on gauge theories, based on taking the action of symmetry transformations directly on the space coordinates. Via this approach the gauge fields are not introduced at the first step, and they can be interpreted as fluctuations around some classical solutions of the model. The new point of view is connected to the lattice formulation of gauge theories, and the parameter of the non-commutativity of the coordinates appears as the lattice spacing parameter. Through the statements concerning the continuum limit of lattice gauge theories, the suggestion arises that the non-commutative spaces are the natural ones to formulate gauge theories at strong coupling. Via this point of view, a close relation between the large-N limit of gauge theories and string theory can be made manifest. Received: 16 June 2000 / Published online: 8 September 2000     

Fermion condensation in the field strength approach to non-abelian yang-mills theories

Within the field strength approach to Yang-Mills theories the fermionic sectors of gauge theories are bosonized for the SU(2) and SU(3) gauge group. The emerging effective meson theories are studied in the tree approximation. In this approximation the original minimal gauge coupling of the quarks to gluons is rendered into an effective local four-fermion interaction with non-trivial Lorentz and gauge structure. The Schwinger-Dyson equation is solved in the strong coupling limit and the quark condensates and constituent masses are evaluated.     

Gauge dependence of ultraviolet behavior of gauge theories

The gauge dependence of ultraviolet behavior of gauge theories is examined on the basis of renormalization-group equation. Non-Abelian gauge theories are confirmed to be asymptotically free in an arbitrary gauge. It is also shown that the effective gauge parameter approaches a finite value in the ultraviolet limit in contrast with the case of QED.     

Theorems for asymptotic safety of gauge theories

We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.     

Dynamical supersymmetry breaking and gauge anomalies

Some aspects of supersymmetric gauge theories and discussed. It is shown that dynamical supersymmetry breaking does not occur in supersymmetric QED in higher dimensions. The cancellation of both local (perturbative) and global (non-perturbative) gauge anomalies are also discussed in supersymmetric gauge theories. We argue that there is no dynamical supersymmetry breaking in higher dimensions in any supersymmetric gauge theories free of gauge anomalies. It is also shown that for supersymmetric gauge theories in higher dimensions with a compact connected simple gauge group, when the local anomaly-free condition is satisfied, there can be at most a possibleZ ₂ global gauge anomaly in extended supersymmetricSO(10) (or spin (10)) gauge theories inD=10 dimensions containing additional Weyl fermions in a spinor representation ofSO(10) (or spin (10)). In four dimensions with local anomaly-free condition satisfied, the only possible global gauge anomalies in supersymmetric gauge theories areZ ₂ global gauge anomalies for extended supersymmetricSP(2N) (N=rank) gauge theories containing additional Weyl fermions in a representation ofSP(2N) with an odd 2nd-order Dynkin index.     

Gauge bosons at zero and finite temperature

Gauge theories of the Yang–Mills type are the single most important building block of the standard model of particle physics and beyond. They are an integral part of the strong and weak interactions, and in their Abelian version of electromagnetism. Since Yang–Mills theories are gauge theories their elementary particles, the gauge bosons, cannot be described without fixing a gauge. Therefore, to obtain their properties a quantized and gauge-fixed setting is necessary.     

Chemical potentials in gauge theories

One-loop calculations of the thermodynamic potential Ω are presented for temperature gauge and non-gauge theories. Prototypical formulae are derived which give Ω as a function of both (i) boson and/or fermion chemical potential, and in the case of gauge theories (ii) the thermal vacuum parameter A₀=const (A_μ is the euclidean gauge potential). From these basic abelian gauge theory formulae, the one-loop contribution to Ω can readily be constructed for Yang-Mills theories, and also for non-gauge theories.     

Is quantum gravity ambiguity-free?

The ultraviolet behaviour of Green functions in the field theories with a local gauge symmetry is, to some extent, gauge dependent. This is due to the intervention of ghost-like gauge degrees of freedom. We argue that it may be possible, in the case of non-polynomial gauge theories, to find a class of gauges in which all ultraviolet divergences and their attendant ambiguities are suppressed.     

On a Mathematical Definition of a Renormalization Transformation for Lattice Gauge Theories

In lattice gauge theories, the renormalization transformation and its properties are formally defined and formally proved by making use of Dirac's function and its properties. In this Letter, we shall give a mathematically rigorous definition of a renormalization transformation for lattice pure gauge field theories and show the required properties, which are use to show ultraviolet stability of lattice gauge theories.     

The action of the group of bundle-automorphisms on the space of connections and the geometry of gauge theories

Some aspects of the geometry of gauge theories are sketched in this review. We deal essentially with Yang-Mills theory, discussing the structure of the space of gauge orbits and the geometrical interpretation of ghosts and anomalies. Occasionally we deal also with classical gauge theories of gravitation and in particular we study the action of the group of diffeomorphisms on the space of linear connections. Finally we comment on the mathematical interpretation of anomalies in field theories.     

On the gauge Potts model and the plaquette percolation problem

It is shown that the ar 1, 0 limit of the Potts gauge model describes plaquette percolation as the analogous limit of the spin model describes bond percolation. These results further strengthen the connection between gauge theories and random surfaces. Moreover, further generalizations to other types of gauge theories are presented.     

Zero-momentum contribution to wilson loops in periodic boxes

We compute the zero-momentum finite-size effects in non-abelian gauge theories. In some cases, these effects are to lowest-order identical for lattice and continuum theories and are of the order of a few percent for an SU(3) gauge theory in four dimensions.     

Remarks on gauge theories of fundamental forces

By clarifying the concepts of strong and weak gravity in a scalar-scalar-tensor theory of gravitation, we have studied an action principle from which we have discussed several theories of weak and (separately) strong gravity. By further appealing to the general principle of gauge invariance we are able to discuss gauge theories of spontaneously broken discrete symmetries. Finally, we find that super-heavy gauge bosons are automatically excluded when both gravities are properly understood.     

Topological Charges in Gauge Theories

Topological and geometric aspects of gauge theories are examined. The geometry of the fiber-bundle formulation of gauge theories is discussed and compared with the formalism of general relativity. The basic role played by the parallel displacement operator of this geometry is examined. With this operator a gauge independent characterization of various topological singularities and non-singular soliton configurations is carried out.     

Geometry and topology of chiral anomalies in gauge theories

Geometrical and topological aspects of chiral anomalies in gauge theories are reviewed. Geometrical and topological concepts and results for chiral anomalies in gauge theories are considered, including differential forms, Lie groups, homotopy, homology, cohomology, Riemannian manifolds, fibre bundles, characteristic classes, index theorems and spectral flow. Gauge theories and their formulation in terms of differential forms and fibre bundles are described. The quantisation of gauge theories is performed using path integrals, and the orbit space, BRST symmetries and ? vacuum are discussed. Gauge theories with fermions are formulated, including realistic models of strong and weak interactions. Chiral anomalies and related issues such as the existence of Schwinger terms, their origins in terms of differential forms, cohomology, the orbit space, BRST identities, Hamiltonian systems and relations to index theorems are analysed. Constraints on models for particle physics from chiral anomalies and theories involving spontaneously broken chiral symmetry described by effective Lagrangians are also mentioned.     

Dispersion relation approach to the anomalous magnetic moment in gauge theories

The reason why the dispersion relations for the anomalous magnetic moment are not valid in gauge theories is explained. New sum rules are derived based on unitary bounds of scattering amplitudes. In gauge theories these sum rules give the correct values for the anomalous magnetic moment, while, in the case of conventional renormalizable theories which contain no massive vector bosons, they are identical with the usual dispersion relations for the anomalous magnetic moment.     

Field theories with no local conservation of the electric charge

The gauge theories with a simply connected gauge group and a disconnected subgroup of unbroken symmetries are studied. It is shown that strings exist in such theories. In some cases a particle changes the sign of its electric charge when it goes around the string.     

Large-N lattice models with mixed actions

U(N) lattice gauge theories and spin systems with mixed fundamental and adjoint representation actions are studied. Exact results are found for two-dimensional gauge theories and one-dimensional spin chains. Phase diagrams for higher-dimensional systems are found using mean field theory. Various implications of this work are discussed.     

Spin and mass content of linearized Poincaré gauge theories

A unified gauge theory of massless and massive spin-2 fields is of considerable current interest. The Poincaré gauge theories with quadratic Lagrangian are linearized, and the conditions on the parameters are found which will lead to viable linear theories with massive gauge particles. As well as the 2⁺ massless gravitons coming from the translational gauge potential, the rotational gauge potentials, in the linearized limit, give rise to 2⁺ and 2⁻ particles of equal mass, as well as a massive pseudoscalar.