Monopole Constituents inside SU(n) Calorons

We present a simple result for the action density of the SU(n) charge one periodic instantons - or calorons - with arbitrary non-trivial Polyakov loop P_oo at spatial infinity. It is shown explicitly that there are n lumps inside the caloron, each of which represents a BPS monopole, their masses being related to the eigenvalues of P_oo. A suitable combination of the ADHM construction and the Nahm transformation is used to obtain this result.Comment: 8 pages, 1 figure (in three parts), late

Orbifold resolutions with general profile

A very general class of resolved versions of the C/Z_N, T^2/Z_N and S^1/Z_2 orbifolds is considered and the free theory of 6D chiral fermions studied on it. As the orbifold limit is taken, localized 4D chiral massless fermions are seen to arise at the fixed points. Their number, location and chirality is found to be independent on the detailed profile of the resolving space and to agree with the result of hep-th/0409229, in which a particular resolution was employed. As a consistency check of the resolution procedure, the massive equation is numerically studied. In particular, for S^1/Z_2, the "resolved" mass--spectrum and wave functions in the internal space are seen to correctly reproduce the usual orbifold ones, as the orbifold limit is taken.Comment: 28 pages, 3 figures, typos corrected, references adde

Laplacian modes probing gauge fields

We show that low-lying eigenmodes of the Laplace operator are suitable to represent properties of the underlying SU(2) lattice configurations. We study this for the case of finite temperature background fields, yet in the confinement phase. For calorons as classical solutions put on the lattice, the lowest mode localizes one of the constituent monopoles by a maximum and the other one by a minimum, respectively. We introduce adjustable phase boundary conditions in the time direction, under which the role of the monopoles in the mode localization is interchanged. Similar hopping phenomena are observed for thermalized configurations. We also investigate periodic and antiperiodic modes of the adjoint Laplacian for comparison. In the second part we introduce a new Fourier-like low-pass filter method. It provides link variables by truncating a sum involving the Laplacian eigenmodes. The filter not only reproduces classical structures, but also preserves the confining potential for thermalized ensembles. We give a first characterization of the structures emerging from this procedure.Comment: 43 pages, 26 figure

Chiral zero-mode for abelian BPS dipoles

We present an exact normalisable zero-energy chiral fermion solution for abelian BPS dipoles. For a single dipole, this solution is contained within the high temperature limit of the SU(2) caloron with non-trivial holonomy.Comment: 9 pages, 1 figure (in 2 parts), presented at the workshop on "Confinement, Topology, and other Non-Perturbative Aspects of QCD", 21-27 Jan. 2002, Stara Lesna, Slovaki

Mass Wasting In Planetary Environments: Implications For Seismicity

On Earth, mass wasting events such as rock falls and landslides are well known conse-quences of seismic activity. Through a variety of re-mote sensing techniques, tectonic faults have been pos-itively identified on all four of the inner planets, Earth's Moon, several outer planet satellites, and aster-oids. High-resolution imaging has furthermore ena-bled positive identification of mass wasting events on many of these bodies. On Mars, it has been suggested that fallen boulders may be indicative of pale-omarsquakes. On the Moon, meteor impacts and moonquakes have likewise been suggested as potential triggering mechanisms for mass wasting. Indeed, we know from the Apollo era that the Moon experienc-es a wide variety of seismicity. Seismicity estimates play an important role in creat-ing regional geological characterizations, which are useful not only for understanding a planet's formation and evolution, but also of key importance to site selec-tion for landed missions. Here we investigate the re-gional effects of seismicity in planetary environments with the goal of determining whether surface features such as landslides and boulder trails on the Moon, Mars, and Mercury could be triggered by fault motion. We attempt to quantify the amount of near-source ground shaking necessary to mobilize the mate-rial observed in various instances of mass wasting

Supersymmetric Lorentz-Covariant Hyperspaces and self-duality equations in dimensions greater than (4|4)

We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel SO(3,1)-covariant superspaces, which we call hyperspaces, having dimensionality greater than (4|4) of traditional super-Minkowski space. As an application, we consider gauge fields on complexifications of these superspaces; and extending the concept of self-duality, we obtain classes of completely solvable equations analogous to the four-dimensional self-duality equations.Comment: 29 pages, late

Democratic Supersymmetry

We present generalisations of N-extended supersymmetry algebras in four dimensions, using Lorentz covariance and invariance under permutation of the N supercharges as selection criteria.Comment: 26 pages, latex fil

The Haldane-Rezayi Quantum Hall State and Conformal Field Theory

We propose field theories for the bulk and edge of a quantum Hall state in the universality class of the Haldane-Rezayi wavefunction. The bulk theory is associated with the $c=-2$ conformal field theory. The topological properties of the state, such as the quasiparticle braiding statistics and ground state degeneracy on a torus, may be deduced from this conformal field theory. The 10-fold degeneracy on a torus is explained by the existence of a logarithmic operator in the $c=-2$ theory; this operator corresponds to a novel bulk excitation in the quantum Hall state. We argue that the edge theory is the $c=1$ chiral Dirac fermion, which is related in a simple way to the $c=-2$ theory of the bulk. This theory is reformulated as a truncated version of a doublet of Dirac fermions in which the $SU(2)$ symmetry -- which corresponds to the spin-rotational symmetry of the quantum Hall system -- is manifest and non-local. We make predictions for the current-voltage characteristics for transport through point contacts.Comment: 37 pages, LaTeX. Some references added, minor changes at the end of section