Proof of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory

We prove the MHV vertex expansion for all tree amplitudes of N=4 SYM theory. The proof uses a shift acting on all external momenta, and we show that every N^kMHV tree amplitude falls off as 1/z^k, or faster, for large z under this shift. The MHV vertex expansion allows us to derive compact and efficient generating functions for all N^kMHV tree amplitudes of the theory. We also derive an improved form of the anti-NMHV generating function. The proof leads to a curious set of sum rules for the diagrams of the MHV vertex expansion.Comment: 40 pages, 7 figure

A super MHV vertex expansion for N=4 SYM theory

We present a supersymmetric generalization of the MHV vertex expansion for all tree amplitudes in N=4 SYM theory. In addition to the choice of a reference spinor, this super MHV vertex expansion also depends on four reference Grassmann parameters. We demonstrate that a significant fraction of diagrams in the expansion vanishes for a judicious choice of these Grassmann parameters, which simplifies the computation of amplitudes. Even pure-gluon amplitudes require fewer diagrams than in the ordinary MHV vertex expansion. We show that the super MHV vertex expansion arises from the recursion relation associated with a holomorphic all-line supershift. This is a supersymmetric generalization of the holomorphic all-line shift recently introduced in arXiv:0811.3624. We study the large-z behavior of generating functions under these all-line supershifts, and find that they generically provide 1/z^k falloff at (Next-to)^k MHV level. In the case of anti-MHV generating functions, we find that a careful choice of shift parameters guarantees a stronger 1/z^(k+4) falloff. These particular all-line supershifts may therefore play an important role in extending the super MHV vertex expansion to N=8 supergravity.Comment: 26 pages, 3 figures, v2: analytic expression for counting of super MHV vertex diagrams added; references adde

On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions

We clarify the notion of the DS --- generalized Drinfeld-Sokolov --- reduction approach to classical ${\cal W}$-algebras. We first strengthen an earlier theorem which showed that an $sl(2)$ embedding ${\cal S}\subset {\cal G}$ can be associated to every DS reduction. We then use the fact that a \W-algebra must have a quasi-primary basis to derive severe restrictions on the possible reductions corresponding to a given $sl(2)$ embedding. In the known DS reductions found to date, for which the \W-algebras are denoted by ${\cal W}_{\cal S}^{\cal G}$-algebras and are called canonical, the quasi-primary basis corresponds to the highest weights of the $sl(2)$. Here we find some examples of noncanonical DS reductions leading to \W-algebras which are direct products of ${\cal W}_{\cal S}^{\cal G}$-algebras and `free field' algebras with conformal weights $\Delta \in \{0, {1\over 2}, 1\}$. We also show that if the conformal weights of the generators of a ${\cal W}$-algebra obtained from DS reduction are nonnegative $\Delta \geq 0$ (which isComment: 48 pages, plain TeX, BONN-HE-93-14, DIAS-STP-93-0

Zero Modes and the Atiyah-Singer Index in Noncommutative Instantons

We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero modes in the adjoint representation and 2k (k) bosonic (fermionic) zero modes in the fundamental representation from the ADHM construction. The number of fermionic zero modes is also shown to be exactly equal to the Atiyah-Singer index of the Dirac operator in the noncommutative instanton background. We point out that (super)conformal zero modes in non-BPS instantons are affected by the noncommutativity. The role of Lorentz symmetry breaking by the noncommutativity is also briefly discussed to figure out the structure of U(1) instantons.Comment: v3: 24 pages, Latex, corrected typos, references added, to appear in Phys. Rev.

Enzymatic removal of cellulose from cotton/polyester fabric blends

The production of light-weight polyester fabrics from a polyester/cotton blended fabric, by means of the enzymatic removal of the cellulosic part of the material, was investigated. The removal of cotton from the blended fabric yielded more than 80% of insoluble microfibrillar material by the combined action of high beating effects and cellulase hydrolysis.Other major features of this enzymatic process for converting cotton fibers into microfibrillar material are bath ratio, enzyme dosage and treatment time

Advances in multispectral and hyperspectral imaging for archaeology and art conservation

Multispectral imaging has been applied to the field of art conservation and art history since the early 1990s. It is attractive as a noninvasive imaging technique because it is fast and hence capable of imaging large areas of an object giving both spatial and spectral information. This paper gives an overview of the different instrumental designs, image processing techniques and various applications of multispectral and hyperspectral imaging to art conservation, art history and archaeology. Recent advances in the development of remote and versatile multispectral and hyperspectral imaging as well as techniques in pigment identification will be presented. Future prospects including combination of spectral imaging with other noninvasive imaging and analytical techniques will be discussed

ADHM Construction of Instantons on the Torus

We apply the ADHM instanton construction to SU(2) gauge theory on T^n x R^(4-n)for n=1,2,3,4. To do this we regard instantons on T^n x R^(4-n) as periodic (modulo gauge transformations) instantons on R^4. Since the R^4 topological charge of such instantons is infinite the ADHM algebra takes place on an infinite dimensional linear space. The ADHM matrix M is related to a Weyl operator (with a self-dual background) on the dual torus tilde T^n. We construct the Weyl operator corresponding to the one-instantons on T^n x R^(4-n). In order to derive the self-dual potential on T^n x R^(4-n) it is necessary to solve a specific Weyl equation. This is a variant of the Nahm transformation. In the case n=2 (i.e. T^2 x R^2) we essentially have an Aharonov Bohm problem on tilde T^2. In the one-instanton sector we find that the scale parameter, lambda, is bounded above, (lambda)^2 tv<4 pi, tv being the volume of the dual torus tilde T^2.Comment: 35 pages, LATeX. New section on Nahm transform included, presentation improved, reference added, to appear in Nuclear Physics