An ideal toy model for confining, walking and conformal gauge theories: the O(3) sigma model with theta-term

A toy model is proposed for four dimensional non-abelian gauge theories coupled to a large number of fermionic degrees of freedom. As the number of flavors is varied the gauge theory may be confining, walking or conformal. The toy model mimicking this feature is the two dimensional O(3) sigma model with a theta-term. For all theta the model is asymptotically free. For small theta the model is confining in the infra red, for theta = pi the model has a non-trivial infra red fixed point and consequently for theta slightly below pi the coupling walks. The first step in investigating the notoriously difficult systematic effects of the gauge theory in the toy model is to establish non-perturbatively that the theta parameter is actually a relevant coupling. This is done by showing that there exist quantities that are entirely given by the total topological charge and are well defined in the continuum limit and are non-zero, despite the fact that the topological susceptibility is divergent. More precisely it is established that the differences of connected correlation functions of the topological charge (the cumulants) are finite and non-zero and consequently there is only a single divergent parameter in Z(theta) but otherwise it is finite. This divergent constant can be removed by an appropriate counter term rendering the theory completely finite even at theta > 0.Comment: 9 pages, 2 figures, minor modification, references adde

Geometry of W-algebras from the affine Lie algebra point of view

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if the W-algebra in question is obtained by reducing a WZNW model. The fields that survive the reduction will obey non-linear Poisson bracket (or commutator) relations in general. For example the Toda models are well-known theories which possess such a non-linear W-symmetry and many features of these models can only be understood if one investigates the reduction procedure. In this paper we analyze the SL(n,R) case from which the so-called W_n-algebras can be obtained. One advantage of the reduction viewpoint is that it gives a constructive way to classify the symplectic leaves of the W-algebra which we had done in the n=2 case which will correspond to the coadjoint orbits of the Virasoro algebra and for n=3 which case gives rise to the Zamolodchikov algebra. Our method in principle is capable of constructing explicit representatives on each leaf. Another attractive feature of this approach is the fact that the global nature of the W-transformations can be explicitly described. The reduction method also enables one to determine the ``classical highest weight (h. w.) states'' which are the stable minima of the energy on a W-leaf. These are important as only to those leaves can a highest weight representation space of the W-algebra be associated which contains a ``classical h. w. state''.Comment: 17 pages, LaTeX, revised 1. and 7. chapter

Calorons with non-trivial holonomy on and off the lattice

We discuss recent solutions for SU(2) calorons with non-trivial holonomy at higher charge, both through analytic means and using cooling, as well as extensive lattice studies for SU(3).Comment: 12 pages, 16 figures in 34 parts, 4 talks presented at Lattice 2004(topology

Spatiotemporal Differences in Gene Expression Between Motor and Sensory Autografts and Their Effect on Femoral Nerve Regeneration in the Rat

To improve the outcome after autologous nerve grafting in the clinic, it is important to understand the limiting variables such as distinct phenotypes of motor and sensory Schwann cells. This study investigated the properties of phenotypically different autografts in a 6 mm femoral nerve defect model in the rat, where the respective femoral branches distally of the inguinal bifurcation served as homotopic, or heterotopic autografts. Axonal regeneration and target reinnervation was analyzed by gait analysis, electrophysiology, and wet muscle mass analysis. We evaluated regeneration-associated gene expression between 5 days and 10 weeks after repair, in the autografts as well as the proximal, and distal segments of the femoral nerve using qRT-PCR. Furthermore we investigated expression patterns of phenotypically pure ventral and dorsal roots. We identified highly significant differences in gene expression of a variety of regeneration-associated genes along the central – peripheral axis in healthy femoral nerves. Phenotypically mismatched grafting resulted in altered spatiotemporal expression of neurotrophic factor BDNF, GDNF receptor GFRα1, cell adhesion molecules Cadm3, Cadm4, L1CAM, and proliferation associated Ki67. Although significantly higher quadriceps muscle mass following homotopic nerve grafting was measured, we did not observe differences in gait analysis, and electrophysiological parameters between treatment paradigms. Our study provides evidence for phenotypic commitment of autologous nerve grafts after injury and gives a conclusive overview of temporal expression of several important regeneration-associated genes after repair with sensory or motor graft

Topology and higher dimensional representations

SU(3) gauge theory in the 2-index symmetric (sextet) and fundamental representations is considered in symmetric and periodic boxes. Using the overlap formulation in the quenched approximation it is shown that the topological charge obtained from the sextet index theorem always leads to an integer value and agrees with the charge obtained from the fundamental index theorem in the continuum. At larger lattice spacing configurations exist with fractional topological charge if the sextet index is used but these are lattice artifacts and the probability of finding such a configuration rapidly approaches zero. By considering the decomposition of the sextet representation with respect to an SU(2) subgroup it is shown that the SU(2) adjoint index theorem leads to integer charge as well. We conclude that the non-zero value of the bilinear gaugino condensate in N=1 super-Yang-Mills theory cannot be attributed to configurations with fractional topological charge once periodic boundary conditions are imposed.Comment: 14 pages, 7 figures; discussion and references adde

A horse’s locomotor signature: COP path determined by the individual limb

Introduction Ground reaction forces in sound horses with asymmetric hooves show systematic differences in the horizontal braking force and relative timing of break-over. The Center Of Pressure (COP) path quantifies the dynamic load distribution under the hoof in a moving horse. The objective was to test whether anatomical asymmetry, quantified by the difference in dorsal wall angle between the left and right forelimbs, correlates with asymmetry in the COP path between these limbs. In addition, repeatability of the COP path was investigated. Methods A larger group (n = 31) visually sound horses with various degree of dorsal hoof wall asymmetry trotted three times over a pressure mat. COP path was determined in a hoof-bound coordinate system. A relationship between correlations between left and right COP paths and degree of asymmetry was investigated. Results Using a hoof-bound coordinate system made the COP path highly repeatable and unique for each limb. The craniocaudal patterns are usually highly correlated between left and right, but the mediolateral patterns are not. Some patterns were found between COP path and dorsal wall angle but asymmetry in dorsal wall angle did not necessarily result in asymmetry in COP path and the same could be stated for symmetry. Conclusion This method is a highly sensitive method to quantify the net result of the interaction between all of the forces and torques that occur in the limb and its inertial properties. We argue that changes in motor control, muscle force, inertial properties, kinematics and kinetics can potentially be picked up at an early stage using this method and could therefore be used as an early detection method for changes in the musculoskeletal apparatus

Spatiotemporal Differences in Gene Expression Between Motor and Sensory Autografts and Their Effect on Femoral Nerve Regeneration in the Rat.

To improve the outcome after autologous nerve grafting in the clinic, it is important to understand the limiting variables such as distinct phenotypes of motor and sensory Schwann cells. This study investigated the properties of phenotypically different autografts in a 6 mm femoral nerve defect model in the rat, where the respective femoral branches distally of the inguinal bifurcation served as homotopic, or heterotopic autografts. Axonal regeneration and target reinnervation was analyzed by gait analysis, electrophysiology, and wet muscle mass analysis. We evaluated regeneration-associated gene expression between 5 days and 10 weeks after repair, in the autografts as well as the proximal, and distal segments of the femoral nerve using qRT-PCR. Furthermore we investigated expression patterns of phenotypically pure ventral and dorsal roots. We identified highly significant differences in gene expression of a variety of regeneration-associated genes along the central - peripheral axis in healthy femoral nerves. Phenotypically mismatched grafting resulted in altered spatiotemporal expression of neurotrophic factor BDNF, GDNF receptor GFRα1, cell adhesion molecules Cadm3, Cadm4, L1CAM, and proliferation associated Ki67. Although significantly higher quadriceps muscle mass following homotopic nerve grafting was measured, we did not observe differences in gait analysis, and electrophysiological parameters between treatment paradigms. Our study provides evidence for phenotypic commitment of autologous nerve grafts after injury and gives a conclusive overview of temporal expression of several important regeneration-associated genes after repair with sensory or motor graft