On the zero of the fermion zero mode

We argue that the fermionic zero mode in non-trivial gauge field backgrounds must have a zero. We demonstrate this explicitly for calorons where its location is related to a constituent monopole. Furthermore a topological reasoning for the existence of the zero is given which therefore will be present for any non-trivial configuration. We propose the use of this property in particular for lattice simulations in order to uncover the topological content of a configuration.Comment: 6 pages, 3 figures in 5 part

Anderson localization through Polyakov loops: lattice evidence and Random matrix model

We investigate low-lying fermion modes in SU(2) gauge theory at temperatures above the phase transition. Both staggered and overlap spectra reveal transitions from chaotic (random matrix) to integrable (Poissonian) behavior accompanied by an increasing localization of the eigenmodes. We show that the latter are trapped by local Polyakov loop fluctuations. Islands of such "wrong" Polyakov loops can therefore be viewed as defects leading to Anderson localization in gauge theories. We find strong similarities in the spatial profile of these localized staggered and overlap eigenmodes. We discuss possible interpretations of this finding and present a sparse random matrix model that reproduces these features.Comment: 11 pages, 23 plots in 11 figures; some comments and references added, some axis labels corrected; journal versio

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

Probing for Instanton Quarks with epsilon-Cooling

We use epsilon-cooling, adjusting at will the order a^2 corrections to the lattice action, to study the parameter space of instantons in the background of non-trivial holonomy and to determine the presence and nature of constituents with fractional topological charge at finite and zero temperature for SU(2). As an additional tool, zero temperature configurations were generated from those at finite temperature with well-separated constituents. This is achieved by "adiabatically" adjusting the anisotropic coupling used to implement finite temperature on a symmetric lattice. The action and topological charge density, as well as the Polyakov loop and chiral zero-modes are used to analyse these configurations. We also show how cooling histories themselves can reveal the presence of constituents with fractional topological charge. We comment on the interpretation of recent fermion zero-mode studies for thermalized ensembles at small temperatures.Comment: 26 pages, 14 figures in 33 part

Rest-to-Rest Trajectory Planning for Underactuated Cable-Driven Parallel Robots

This article studies the trajectory planning for underactuated cable-driven parallel robots (CDPRs) in the case of rest-to-rest motions, when both the motion time and the path geometry are prescribed. For underactuated manipulators, it is possible to prescribe a control law only for a subset of the generalized coordinates of the system. However, if an arbitrary trajectory is prescribed for a suitable subset of these coordinates, the constraint deficiency on the end-effector leads to the impossibility of bringing the system at rest in a prescribed time. In addition, the behavior of the system may not be stable, that is, unbounded oscillatory motions of the end-effector may arise. In this article, we propose a novel trajectory-planning technique that allows the end effector to track a constrained geometric path in a specified time, and allows it to transition between stable static poses. The design of such a motion is based on the solution of a boundary value problem, aimed at a finding solution to the differential equations of motion with constraints on position and velocity at start and end times. To prove the effectiveness of such a method, the trajectory planning of a six-degrees-of-freedom spatial CDPR suspended by three cables is investigated. Trajectories of a reference point on the moving platform are designed so as to ensure that the assigned path is tracked accurately, and the system is brought to a static condition in a prescribed time. Experimental validation is presented and discussed

A ring of instantons inducing a monopole loop

We consider the superposition of infinitely many instantons on a circle in R^4. The construction yields a self-dual solution of the Yang-Mills equations with action density concentrated on the ring. We show that this configuration is reducible in which case magnetic charge can be defined in a gauge invariant way. Indeed, we find a unit charge monopole (worldline) on the ring. This is an analytic example of the correlation between monopoles and action/topological density, however with infinite action. We show that both the Maximal Abelian Gauge and the Laplacian Abelian Gauge detect the monopole, while the Polyakov gauge does not. We discuss the implications of this configuration.Comment: 11 pages, 1 figur

Gluino zero-modes for non-trivial holonomy calorons

We couple fermion fields in the adjoint representation (gluinos) to the SU(2) gauge field of unit charge calorons defined on R^3 x S_1. We compute corresponding zero-modes of the Dirac equation. These are relevant in semiclassical studies of N=1 Super-symmetric Yang-Mills theory. Our formulas, show that, up to a term proportional to the vector potential, the modes can be constructed by different linear combinations of two contributions adding up to the total caloron field strength.Comment: 17 pages, 3 Postscript figures, late

A gauge-invariant object in non-Abelian gauge theory

We propose a nonlocal definition of a gauge-invariant object in terms of the Wilson loop operator in a non--Abelian gauge theory. The trajectory is a closed curve defined by an (untraced) Wilson loop which takes its value in the center of the color group. We show that definition shares basic features with the gauge-dependent 't Hooft construction of Abelian monopoles in Yang-Mills theories. The chromoelectric components of the gluon field have a hedgehog-like behavior in the vicinity of the object. This feature is dual to the structure of the 't Hooft-Polyakov monopoles which possesses a hedgehog in the magnetic sector. A relation to color confinement and lattice implementation of the proposed construction are discussed.Comment: 11 pages, 2 figures, RevTeX4; references added, substantial revisions, replaced to match version accepted for publicatio