Zero Point Energy of Renormalized Wilson Loops

The quark antiquark potential, and its associated zero point energy, can be extracted from lattice measurements of the Wilson loop. We discuss a unique prescription to renormalize the Wilson loop, for which the perturbative contribution to the zero point energy vanishes identically. A zero point energy can arise nonperturbatively, which we illustrate by considering effective string models. The nonperturbative contribution to the zero point energy vanishes in the Nambu model, but is nonzero when terms for extrinsic curvature are included. At one loop order, the nonperturbative contribution to the zero point energy is negative, regardless of the sign of the extrinsic curvature term.Comment: 14 pages, ReVTeX. Paper shortened, results unchange

Systematic U(1)_{B-L} Extensions of Loop-Induced Neutrino Mass Models with Dark Matter

We study the gauged U(1)_{B-L} extensions of the models for neutrino masses and dark matter. In this class of models, tiny neutrino masses are radiatively induced through the loop diagrams, while the origin of the dark matter stability is guaranteed by the remnant of the gauge symmetry. Depending on how the lepton number is violated in the neutrino mass diagrams, these models are systematically classified. We present a complete list for the one-loop Z_2 and the two-loop Z_3 neutrino mass models as examples of the classification. These underlying gauge symmetries and its breaking patterns can be probed at future high energy colliders by looking at the width of the new gauge boson.Comment: 15 pages, 4 figures, revised to match version published in PR

A Two-loop Test of Buscher's T-duality I

We study the two loop quantum equivalence of sigma models related by Buscher's T-duality transformation. The computation of the two loop perturbative free energy density is performed in the case of a certain deformation of the SU(2) principal sigma model, and its T-dual, using dimensional regularization and the geometric sigma model perturbation theory. We obtain agreement between the free energy density expressions of the two models.Comment: 28 pp, Latex, references adde

Loop groups and noncommutative geometry

We describe the representation theory of loop groups in terms of K-theory and noncommutative geometry. This is done by constructing suitable spectral triples associated with the level l projective unitary positive-energy representations of any given loop group $LG$. The construction is based on certain supersymmetric conformal field theory models associated with LG in the setting of conformal nets. We then generalize the construction to many other rational chiral conformal field theory models including coset models and the moonshine conformal net.Comment: Revised versio

Phenomenological Equations of State for the Quark-Gluon Plasma

Two phenomenological models describing an SU(N) quark-gluon plasma are presented. The first is obtained from high temperature expansions of the free energy of a massive gluon, while the second is derived by demanding color neutrality over a certain length scale. Each model has a single free parameter, exhibits behavior similar to lattice simulations over the range T_d - 5T_d, and has the correct blackbody behavior for large temperatures. The N = 2 deconfinement transition is second order in both models, while N = 3,4, and 5 are first order. Both models appear to have a smooth large-N limit. For N >= 4, it is shown that the trace of the Polyakov loop is insufficient to characterize the phase structure; the free energy is best described using the eigenvalues of the Polyakov loop. In both models, the confined phase is characterized by a mutual repulsion of Polyakov loop eigenvalues that makes the Polyakov loop expectation value zero. In the deconfined phase, the rotation of the eigenvalues in the complex plane towards 1 is responsible for the approach to the blackbody limit over the range T_d - 5T_d. The addition of massless quarks in SU(3) breaks Z(3) symmetry weakly and eliminates the deconfining phase transition. In contrast, a first-order phase transition persists with sufficiently heavy quarks.Comment: 22 pages, RevTeX, 9 eps file