Hausdorff dimensions and gauge theories (original) (raw)

Surplus Anomaly and Random Geometries

1998

Four dimensional simplicial gravity has been studied by means of Monte Carlo simulations for some time1 and an extensive numerical documentation of the properties of the model has been gathered. The main outcome of the studies is that the model undergoes a discontinuous phase transition2 between the elongated and the crumpled phase when one changes the coupling to curvature. In the crumpled phase there are singular vertices in the system having orders growing extensively with the volume of the system3.

U() gauge theory and lattice strings

Nucl Phys B, 1994

The U(N) gauge theory on a D-dimensional lattice is reformulated as a theory of lattice strings (a statistical model of random surfaces). The Boltzmann weights of the surfaces can have both signs and are tuned so that the longitudinal modes of the string are elliminated. The U(\infty) gauge theory is described by noninteracting planar surfaces and the 1/N corrections are produced by surfaces with higher topology as well as by contact interactions due to microscopic tubes, trousers, handles, etc. We pay special attention to the case D=2 where the sum over surfaces can be performed explicitly, and demonstrate that it reproduces the known exact results for the free energy and Wilson loops in the continuum limit. In D=4 dimensions, our lattice string model reproduces the strong coupling phase of the gauge theory. The weak coupling phase is described by a more complicated string whose world surface may have windows. A possible integration measure in the space of continuous surfaces is suggested.

Nonperturbative definition of five-dimensional gauge theories on the R 4 � S 1 / Z 2 orbifold

Nucl Phys B, 2005

We construct a Z_2 orbifold projection of SU(N) gauge theories formulated in five dimensions with a compact fifth dimension. We show through a non-perturbative argument that no boundary mass term for the Higgs field, identified with some of the fifth dimensional components of the gauge field, is generated, which would be quadratically divergent in the five-dimensional ultraviolet cutoff. This opens the possibility of studying these theories non-perturbatively in order to establish if they can be used as effective weakly interacting theories at low energies. We make preparations for a study on the lattice. In particular we show that only Dirichlet boundary conditions are needed, which specify the breaking pattern of the gauge group at the orbifold fixpoints.