Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators with two supercharges, for world-volume gauge theories of $N$ D-brane probes for both $N \to \infty$ and finite $N$. The techniques are applicable to generic singularities, orbifold, toric, non-toric, complete intersections, et cetera, even to geometries whose precise field theory duals are not yet known. The so-called ``Plethystic Exponential'' provides a simple bridge between (1) the defining equation of the Calabi-Yau, (2) the generating function of single-trace BPS operators and (3) the generating function of multi-trace operators. Mathematically, fascinating and intricate inter-relations between gauge theory, algebraic geometry, combinatorics and number theory exhibit themselves in the form of plethystics and syzygies.Comment: 59+1 pages, 7 Figure

Complete measurement of molecular Coulomb-explosions

Werner U, Lutz HO. Complete measurement of molecular Coulomb-explosions. In: Dube LJ, Mitchell JBA, McKonkey JW, Brion CE, eds. The Physics of Electronic and Atomic Collisions, Invited Papers of XIX ICPEAC Conference. New York: AIP Press; 1995: 741-751

Studying the electronic structure of molecules with high harmonic spectroscopy

High harmonic spectroscopy is a tool to study the valence electronic structure of atoms and molecules. It uses the techniques of high harmonic generation, in which a femtosecond laser ionizes the gas sample and XUV radiation is emitted in the forward direction. The XUV intensity, phase and polarization contain information about the orbital from which an electron was removed by the laser. High harmonic spectroscopy reveals details of electron-electron interactions, motion of electronic wave packets, and can follow a chemical reaction. \ua9 Springer-Verlag Berlin Heidelberg 2013.Peer reviewed: YesNRC publication: Ye