Center Vortices, Nexuses, and Fractional Topological Charge

It has been remarked in several previous works that the combination of center vortices and nexuses (a nexus is a monopole-like soliton whose world line mediates certain allowed changes of field strengths on vortex surfaces) carry topological charge quantized in units of 1/N for gauge group SU(N). These fractional charges arise from the interpretation of the standard topological charge integral as a sum of (integral) intersection numbers weighted by certain (fractional) traces. We show that without nexuses the sum of intersection numbers gives vanishing topological charge (since vortex surfaces are closed and compact). With nexuses living as world lines on vortices, the contributions to the total intersection number are weighted by different trace factors, and yield a picture of the total topological charge as a linking of a closed nexus world line with a vortex surface; this linking gives rise to a non-vanishing but integral topological charge. This reflects the standard 2\pi periodicity of the theta angle. We argue that the Witten-Veneziano relation, naively violating 2\pi periodicity, scales properly with N at large N without requiring 2\pi N periodicity. This reflects the underlying composition of localized fractional topological charge, which are in general widely separated. Some simple models are given of this behavior. Nexuses lead to non-standard vortex surfaces for all SU(N) and to surfaces which are not manifolds for N>2. We generalize previously-introduced nexuses to all SU(N) in terms of a set of fundamental nexuses, which can be distorted into a configuration resembling the 't Hooft-Polyakov monopole with no strings. The existence of localized but widely-separated fractional topological charges, adding to integers only on long distance scales, has implications for chiral symmetry breakdown.Comment: 15 pages, revtex, 6 .eps figure

A conjecture on the infrared structure of the vacuum Schrodinger wave functional of QCD

The Schrodinger wave functional for the d=3+1 SU(N) vacuum is a partition function constructed in d=4; the exponent 2S in the square of the wave functional plays the role of a d=3 Euclidean action. We start from a gauge-invariant conjecture for the infrared-dominant part of S, based on dynamical generation of a gluon mass M in d=4. We argue that the exact leading term, of O(M), in an expansion of S in inverse powers of M is a d=3 gauge-invariant mass term (gauged non-linear sigma model); the next leading term, of O(1/M), is a conventional Yang-Mills action. The d=3 action that is the sum of these two terms has center vortices as classical solutions. The d=3 gluon mass, which we constrain to be the same as M, and d=3 coupling are related through the conjecture to the d=4 coupling strength, but at the same time the dimensionless ratio in d=3 of mass to coupling squared can be estimated from d=3 dynamics. This allows us to estimate the QCD coupling $\alpha_s(M^2)$ in terms of this strictly d=3 ratio; we find a value of about 0.4, in good agreement with an earlier theoretical value but a little low compared to QCD phenomenology. The wave functional for d=2+1 QCD has an exponent that is a d=2 infrared-effective action having both the gauge-invariant mass term and the field strength squared term, and so differs from the conventional QCD action in two dimensions, which has no mass term. This conventional d=2 QCD would lead in d=3 to confinement of all color-group representations. But with the mass term (again leading to center vortices), N-ality = 0 mod N representations are not confined.Comment: 15 pages, no figures, revtex

Computing the Effective Hamiltonian of Low-Energy Vacuum Gauge Fields

A standard approach to investigate the non-perturbative QCD dynamics is through vacuum models which emphasize the role played by specific gauge field fluctuations, such as instantons, monopoles or vortexes. The effective Hamiltonian describing the dynamics of the low-energy degrees of freedom in such approaches is usually postulated phenomenologically, or obtained through uncontrolled approximations. In a recent paper, we have shown how lattice field theory simulations can be used to rigorously compute the effective Hamiltonian of arbitrary vacuum models by stochastically performing the path integral over all the vacuum field fluctuations which are not explicitly taken into account. In this work, we present the first illustrative application of such an approach to a gauge theory and we use it to compute the instanton size distribution in SU(2) gluon-dynamics in a fully model independent and parameter-free way.Comment: 10 pages, 4 figure

The heavy quark decomposition of the S-matrix and its relation to the pinch technique

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0

On a class of embeddings of massive Yang-Mills theory

A power-counting renormalizable model into which massive Yang-Mills theory is embedded is analyzed. The model is invariant under a nilpotent BRST differential s. The physical observables of the embedding theory, defined by the cohomology classes of s in the Faddeev-Popov neutral sector, are given by local gauge-invariant quantities constructed only from the field strength and its covariant derivatives.Comment: LATEX, 34 pages. One reference added. Version published in the journa

Speculations on Primordial Magnetic Helicity

We speculate that above or just below the electroweak phase transition magnetic fields are generated which have a net helicity (otherwise said, a Chern-Simons term) of order of magnitude $N_B + N_L$, where $N_{B,L}$ is the baryon or lepton number today. (To be more precise requires much more knowledge of B,L-generating mechanisms than we currently have.) Electromagnetic helicity generation is associated (indirectly) with the generation of electroweak Chern-Simons number through B+L anomalies. This helicity, which in the early universe is some 30 orders of magnitude greater than what would be expected from fluctuations alone in the absence of B+L violation, should be reasonably well-conserved through the evolution of the universe to around the times of matter dominance and decoupling, because the early universe is an excellent conductor. Possible consequences include early structure formation; macroscopic manifestations of CP violation in the cosmic magnetic field (measurable at least in principle, if not in practice); and an inverse-cascade dynamo mechanism in which magnetic fields and helicity are unstable to transfer to larger and larger spatial scales. We give a quasi-linear treatment of the general-relativistic MHD inverse cascade instability, finding substantial growth for helicity of the assumed magnitude out to scales $\sim l_M\epsilon^{-1}$, where $\epsilon$ is roughly the B+L to photon ratio and $l_M$ is the magnetic correlation length. We also elaborate further on an earlier proposal of the author for generation of magnetic fields above the EW phase transition.Comment: Latex, 23 page

Baryon number non-conservation and phase transitions at preheating

Certain inflation models undergo pre-heating, in which inflaton oscillations can drive parametric resonance instabilities. We discuss several phenomena stemming from such instabilities, especially in weak-scale models; generically, these involve energizing a resonant system so that it can evade tunneling by crossing barriers classically. One possibility is a spontaneous change of phase from a lower-energy vacuum state to one of higher energy, as exemplified by an asymmetric double-well potential with different masses in each well. If the lower well is in resonance with oscillations of the potential, a system can be driven resonantly to the upper well and stay there (except for tunneling) if the upper well is not resonant. Another example occurs in hybrid inflation models where the Higgs field is resonant; the Higgs oscillations can be transferred to electroweak (EW) gauge potentials, leading to rapid transitions over sphaleron barriers and consequent B+L violation. Given an appropriate CP-violating seed, we find that preheating can drive a time-varying condensate of Chern-Simons number over large spatial scales; this condensate evolves by oscillation as well as decay into modes with shorter spatial gradients, eventually ending up as a condensate of sphalerons. We study these examples numerically and to some extent analytically. The emphasis in the present paper is on the generic mechanisms, and not on specific preheating models; these will be discussed in a later paper.Comment: 10 pages, 7 figures included, revtex, epsf, references adde

CSU FIRE 2 cirrus field experiment: Description of field deployment phase

The Colorado State University (CSU) surface observing systems are described. These systems were deployed at the Parsons, Kansas site during the FIRE 2 Cirrus Special Observing Period (SOP) from 13 Nov. - 7 Dec. 1991. The geographical coordinates of the site containing most of the CSU instrumentation are 37 deg. 18 min N. latitude and 96 deg. 30 min. W. longitude; site elevation was 269 meters. In addition, one surface meteorological and broadband flux observing site was maintained at the Tri City Airport which is approximately 18 miles due west of Parsons (37 deg. 20 min. N. latitude, 95 deg. 30 min. 30 sec. W. longitude). A map of the locations of the CSU deployment sites is presented. At the main Parsons site, the instrumentation was located directly adjacent to and north of a lake. Under most cirrus observing conditions, when the wing had a significant southernly component, the lake was upwind of the observing site. The measurements and observations collected during the experiment are listed. These measurements may be grouped into five categories: surface meteorology; infrared spectral and broadband measurements; solar spectral and broadband measurements; upper air measurements; and cloud measurements. A summary of observations collected at the Parsons site during the SOP are presented. The wind profiler, laser ceilometer, surface meteorology and surface broadband radiation instrumentation were operated on a continuous basis. All other systems were operated on an 'on demand' basis when cloud conditions merited the collection of data