Supersymmetric Yang-Mills Theory as Higher Chern-Simons Theory

We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.Comment: v2: 25 pages, conventions improved, typos fixed, published versio

Towards time-dependent, non-equilibrium charge-transfer force fields: Contact electrification and history-dependent dissociation limits

Force fields uniquely assign interatomic forces for a given set of atomic coordinates. The underlying assumption is that electrons are in their quantum-mechanical ground state or in thermal equilibrium. However, there is an abundance of cases where this is unjustified because the system is only locally in equilibrium. In particular, the fractional charges of atoms, clusters, or solids tend to not only depend on atomic positions but also on how the system reached its state. For example, the charge of an isolated solid -- and thus the forces between atoms in that solid -- usually depends on the counterbody with which it has last formed contact. Similarly, the charge of an atom, resulting from the dissociation of a molecule, can differ for different solvents in which the dissociation took place. In this paper we demonstrate that such charge-transfer history effects can be accounted for by assigning discrete oxidation states to atoms. With our method, an atom can donate an integer charge to another, nearby atom to change its oxidation state as in a redox reaction. In addition to integer charges, atoms can exchange "partial charges" which are determined with the split charge equilibration method.Comment: 11 pages, 7 figure

Contact mechanics of and Reynolds flow through saddle points: On the coalescence of contact patches and the leakage rate through near-critical constrictions

We study numerically local models for the mechanical contact between two solids with rough surfaces. When the solids softly touch either through adhesion or by a small normal load $L$, contact only forms at isolated patches and fluids can pass through the interface. When the load surpasses a threshold value, $L_c$, adjacent patches coalesce at a critical constriction, i.e., near points where the interfacial separation between the undeformed surfaces forms a saddle point. This process is continuous without adhesion and the interfacial separation near percolation is fully defined by scaling factors and the sign of $L_c-L$. The scaling factors lead to a Reynolds flow resistance which diverges as $(L_c-L)^\beta$ with $\beta = 3.45$. Contact merging and destruction near saddle points becomes discontinuous when either short-range adhesion or specific short-range repulsion are added to the hard-wall repulsion. These results imply that coalescence and break-up of contact patches can contribute to Coulomb friction and contact aging.Comment: 6 pages, 6 figures, submitted to Euro. Phys. Let

Twistors and Aspects of Integrability of self-dual SYM Theory

With the help of the Penrose-Ward transform, which relates certain holomorphic vector bundles over the supertwistor space to the equations of motion of self-dual SYM theory in four dimensions, we construct hidden infinite-dimensional symmetries of the theory. We also present a new and shorter proof (cf. hep-th/0412163) of the relation between certain deformation algebras and hidden symmetry algebras. This article is based on a talk given by the author at the Workshop on Supersymmetries and Quantum Symmetries 2005 at the BLTP in Dubna, Russia.Comment: 1+7 pages, based on a talk given at the International Workshop "Supersymmetries and Quantum Symmetries" (SQS'05), Dubna, July 27-31 2005; to appear in the proceeding

Low-temperature infrared dielectric function of hyperbolic α\alpha-quartz

We report the infrared dielectric properties of $\alpha$-quartz in the temperature range from $1.5\ \mathrm{K}$ to $200\ \mathrm{K}$. Using an infrared free-electron laser, far-infrared reflectivity spectra of a single crystal $y$-cut were acquired along both principal axes, under two different incidence angles, in S- and P-polarization. These experimental data have been fitted globally for each temperature with a multioscillator model, allowing to extract frequencies and damping rates of the ordinary and extraordinary, transverse and longitudinal optic phonon modes, and hence the temperature-dependent dispersion of the infrared dielectric function. The results are in line with previous high-temperature studies, allowing for a parametrized description of all temperature-dependent phonon parameters and the resulting dielectric function from $1.5\ \mathrm{K}$ up to the $\alpha$-$\beta$-phase transition temperature, $T_C = 846\ \mathrm{K}$. Using these data, we predict remarkably high quality factors for polaritons in $\alpha$-quartz's hyperbolic spectral region at low temperatures