Theodore J. Allen

TOPOLOGICAL MASS GENERATION IN 3+1 DIMENSIONS

The 4-dimensional theory of a 1-form Abelian gauge field A coupled to a 2-form (antisymmetric tensor) potential B is studied. The two gauge invariances of the theory admit a coupling mB ∧ F where F is the field strength (F=dA) of A. It is shown that this theory is a unitary, renormalizable theory of a massive spin-one field with no additional degrees of freedom. In this sense, it is a generalization to four dimensions of topological mechanisms in two dimensions (the Schwinger model) and three dimensions (Chern-Simons theory). The issue of spontaneous symmetry breaking is also examined.

Non-gaussian density perturbations in inflationary cosmologies☆

Abstract The primordial mass density fluctuations may have arisen from quantum fluctuations in a (massless) scalar field that occurred during an inflationary era. We show that it is possible for primordial mass density fluctuations, which arose in this way, to be highly non-gaussian. We also show that the “bad” infrared properties of the propagator for a massless scalar field in de Sitter space can translate itself into a power spectrum, for the two-point spatial correlation of objects that do not trace the mass, which behaves like k −3 , at small wave numbers k .

Axionic black holes from massive axions

Abstract A black hole may carry axionic charge in a theory which has gravity coupled to a massless two-form Kalb-Ramond field. We show that this effect persists if the axion has a topological mass term coupling the Kalb-Ramond potential to a U(1) gauge field. Such mass terms arise in the low-energy effective theory of the string.

Excited glue and the vibrating flux tube

Abstract Recent lattice results for the energy of gluonic excitations as a function of quark separation are shown to correspond to transverse relativistic flux tube vibration modes. For large quark separations all states appear to degenerate into a few categories which are predicted uniquely, given the ground state.

Analytic quantization of the QCD string

We perform an analytic semi-classical quantization of the straight QCD string with one end fixed and a massless quark on the other, in the limits of orbital and radial dominant motion. We compare our results to the exact numerical semi-classical quantization. We observe that the numerical semi-classical quantization agrees well with our exact numerical canonical quantization.

Reduction of the QCD string to a time component vector potential

We demonstrate the equivalence of the relativistic flux tube model of mesons to a simple potential model in the regime of large radial excitation. We make no restriction on the quark masses; either quark may have a zero or finite mass. Our primary result shows that for fixed angular momentum and large radial excitation, the flux tube or QCD string meson with a short-range Coulomb interaction is described by a spinless Salpeter equation with a time component vector potential

From scalar to string confinement

V(r)=ar\ensuremath{-}k/r.

Curved QCD string dynamics

We outline a connection between scalar quark confinement, a phenomenologically successful concept heretofore lacking fundamental justification, and QCD. Although scalar confinement does not follow from QCD, there is an interesting and close relationship between them. We develop a simple model intermediate between scalar confinement and the QCD string for illustrative purposes. Finally, we find analytically the bound state spectrum of the light degrees of freedom for a spinless, massless quark in scalar, time-component vector, and string confinement through semi-classical quantization.

Adiabatic string shape for nonuniform rotation

The concept of Lorentz scalar quark confinement has a long history and is still widely used despite its well-known theoretical faults. We point out here that the predictions of scalar confinement also conflict directly with experiment. We investigate the dependence of heavy-light meson mass differences on the mass of the light quark. In particular, we examine the strange and nonstrange D mesons. We find that the predictions of scalar confinement are in considerable conflict with measured values.