Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills

Using cutting techniques we obtain the two-loop N=4 super-Yang-Mills helicity amplitudes for four-gluon scattering in terms of scalar integral functions. The N=4 amplitudes are considerably simpler than corresponding QCD amplitudes and therefore provide a testing ground for exploring two-loop amplitudes. The amplitudes are constructed directly in terms of gauge invariant quantities and therefore remain relatively compact throughout the calculation. We also present a conjecture for the leading color four-gluon amplitudes to all orders in the perturbative expansion.Comment: Latex, 13 pages, 9 figures, minor changes to signs in eq.(14

Two-Loop N=4 Supersymmetric Amplitudes and QCD

Two-loop four-gluon N=4 susy amplitudes are evaluated via cutting techniques as a testing ground for QCD. A conjecture for four-point amplitudes to all loop orders is described. We also present a new conjecture for the leading-color part of the two-loop five-gluon amplitudes.Comment: Talk presented at 5th International Workshop on Deep Inelastic Scattering and QCD, April 14-18, 1997, 5 page

Defining the Force between Separated Sources on a Light Front

The Newtonian character of gauge theories on a light front requires that the longitudinal momentum P^+, which plays the role of Newtonian mass, be conserved. This requirement conflicts with the standard definition of the force between two sources in terms of the minimal energy of quantum gauge fields in the presence of a quark and anti-quark pinned to points separated by a distance R. We propose that, on a light front, the force be defined by minimizing the energy of gauge fields in the presence of a quark and an anti-quark pinned to lines (1-branes) oriented in the longitudinal direction singled out by the light front and separated by a transverse distance R. Such sources will have a limited 1+1 dimensional dynamics. We study this proposal for weak coupling gauge theories by showing how it leads to the Coulomb force law. For QCD we also show how asymptotic freedom emerges by evaluating the S-matrix through one loop for the scattering of a particle in the N_c representation of color SU(N_c) on a 1-brane by a particle in the \bar N_c representation of color on a parallel 1-brane separated from the first by a distance R<<1/Lambda_{QCD}. Potential applications to the problem of confinement on a light front are discussed.Comment: LaTeX, 15 pages, 12 figures; minor typos corrected; numerical correction in equation 3.

Spontaneous Symmetry Breaking at Infinite Momentum without P+ Zero-Modes

The nonrelativistic interpretation of quantum field theory achieved by quantization in an infinite momentum frame is spoiled by the inclusion of a mode of the field carrying p+=0. We therefore explore the viability of doing without such a mode in the context of spontaneous symmetry breaking (SSB), where its presence would seem to be most needed. We show that the physics of SSB in scalar quantum field theory in 1+1 space-time dimensions is accurately described without a zero-mode.Comment: LaTeX, 8 pages, 3 eps figure

Ultra-violet structure of supergravity theories

We examine the ultraviolet behaviour of supergravity theories as a function of dimension and number of supercharges. We do so by the computation of one and two-loop physical on-shell four point amplitudes. For maximal supergravity, our computations prove the non-renomalisability of supergravity for $D \geq 6$ (including the maximal D=11 case) and give strong evidence for the existance of a five-loop counterterm in D=4. For type I supergravity our results indicate similar patterns. e shall also explore a remarkable relationship between gravity amplitudes and those of Yang-Mills theories. In many ways gravity calculations discover features which relate to the equivalent Yang-Mills features by a squaring proceedure

Shape-based peak identification for ChIP-Seq

We present a new algorithm for the identification of bound regions from ChIP-seq experiments. Our method for identifying statistically significant peaks from read coverage is inspired by the notion of persistence in topological data analysis and provides a non-parametric approach that is robust to noise in experiments. Specifically, our method reduces the peak calling problem to the study of tree-based statistics derived from the data. We demonstrate the accuracy of our method on existing datasets, and we show that it can discover previously missed regions and can more clearly discriminate between multiple binding events. The software T-PIC (Tree shape Peak Identification for ChIP-Seq) is available at http://math.berkeley.edu/~vhower/tpic.htmlComment: 12 pages, 6 figure