Particle theory

Abstract:

We compare the mass spectra and string tensions of SU(2), SU(3) and SU(4) gauge theories in 2+1 dimensions. We find that the ratios of masses are, to a first approximation, independent of Nc and that the remaining dependence can be accurately reproduced by a simple O(1/N2c) correction. This provides us with a prediction of these mass ratios for all SU(Nc) theories in 2+1 dimensions and demonstrates that these theories are 'close' to Nc = ∞ for Nc ≥ 2. We also find that, when expressed in units of the dynamical length scale of the theory, the dimensionful coupling g2 is proportional to 1/Nc at large Nc. We confirm that these theories are indeed confining in the limit Nc → ∞. We describe preliminary calculations in 3+1 dimensions which indicate that the same will be true there. © 1997 Elsevier Science B.V.

Abstract:

We consider new objects in bosonic open string theory -- ND tadpoles, which have N(euman) boundary conditions at one end of the world-sheet and D(irichlet) at the other, must exist due to s-t duality in a string theory with both NN strings and D-branes. We demonstrate how to interpolate between N and D boundary conditions. In the case of mixed boundary conditions the action for a quantum particle is induced on the boundary. Quantum-mechanical particle-wave duality, a dual description of a quantum particle in either the coordinate or the momentum representation, is induced by world-sheet T-duality. The famous relation between compactification radii is equivalent to the quantization of the phase space area of a Planck cell. We also introduce a boundary operator - a ``Zipper'' which changes the boundary condition from N into D and vice versa.

Abstract:

The phase diagram is investigated for SU(2) lattice gauge theory in d = 3, coupled to adjoint scalars. For small values of the quartic scalar coupling, λ, the transition separating Higgs and confinement phases is found to be first-order, in agreement with earlier work by Nadkarni. The surface of second-order transitions conjectured by Nadkarni, however, is shown instead to correspond to crossover behaviour. This conclusion is based on a finite size analysis of the scalar mass and susceptibility. The nature of the phase transition at the termination of first-order behaviour is investigated and we find evidence for a critical point at which the scalar mass vanishes. The photon mass and confining string tension are measured and are found to be negligibly small in the Higgs phase. This is correlated with the very small density of magnetic monopoles in the Higgs phase. The string tension and photon mass rise rapidly as the crossover is traversed towards the symmetric phase. © 1997 Elsevier Science B.V.