18236433
The Elliptic Scattering Theory of the 1/2-XYZ and Higher Order Deformed Virasoro Algebras
Abstract.Bound state excitations of the spin 1/2-XYZ model are considered inside the Bethe Ansatz framework by exploiting the equivalent Non-Linear Integral Equations. Of course, these bound states go to the sine-Gordon breathers in the suitable limit and therefore the scattering factors between them are explicitly computed by inspecting the corresponding Non-Linear Integral Equations. As a consequence, abstracting from the physical model the Zamolodchikov-Faddeev algebra of two n-th elliptic breathers defines a tower of n-order Deformed Virasoro Algebras, reproducing the n = 1 case the usual well-known algebra of Shiraishi-Kubo-Awata-Odake [1].Communicated by Vincent Rivasseau
118791067
On the logarithmic powers of sl(2) SYM(4)
In the high spin limit the minimal anomalous dimension of (fixed) twist operators in the $sl(2)$ sector of planar ${\cal N}=4$ Super Yang-Mills theory expands as $\gamma(g,s,L)=f(g) \ln s + f_{sl}(g,L) + \sum \limits_{n=1}^\infty \gamma^{(n)}(g,L) (\ln s)^{-n} + ... $. We find that the sub-logarithmic contribution $\gamma^{(n)}(g,L) $ is governed by a linear integral equation, depending on the solution of the linear integral equations appearing at the steps $n'\leq n-3$. We work out this recursive procedure and determine explicitly $\gamma^{(n)}(g,L) $ (in particular $\gamma^{(1)}(g,L)=0$ and $\gamma^{(n)}(g,2)=\gamma^{(n)}(g,3)=0$). Furthermore, we connect the $\gamma^{(n)}(g,L) $ (for finite $L$) to the generalised scaling functions, $f^{(r)}_n(g)$, appearing in the limit of large twist $L\sim\ln s$. Finally, we provide the first orders of weak and strong coupling for the first $\gamma^{(n)}(g,L)$ (and hence $f^{(r)}_n(g)$).
16779871
Deformed W N Algebras from Elliptic Sl(n ) Algebras
We extend to the sl(N) case the results that we previously obtained on the construction of W q,p algebras from the elliptic algebra A q,p (sl(2) c). The elliptic algebra A q,p (sl(N) c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N (N − 1)/2 integers, defining q-deformations of the W N algebra, are constructed. The operators t(z) also close an exchange algebra when (−p 1 2) N M = q −c−N for M ∈ Z. It becomes Abelian when in addition p = q N h where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W N algebras depending on the parity of h, characterizing the exchange structures at p = q N h as new W q,p (sl(N)) algebras. Résumé Nousétendons au cas sl(N) les résultats que nous avons obtenus précédemment concernant la construction des algèbres W q,p ` a partir de l'algèbre elliptique A q,p (sl(2) c). L'algèbre elliptique A q,p (sl(N) c) au niveau critique c = −N possède un centré etendu contenant des opérateurs de trace t(z). On construit sur ce centre des familles de structures de Poisson indicées par N (N − 1)/2 entiers, définissant des q-déformations de l'algèbre W N. Les opérateurs t(z) engendrent une algèbre d'´ echange lorsque (−p 1 2) N M = q −c−N o` u M ∈ Z. Cette algèbre devient abélienne si de plus p = q N h avec h entier non nul. Les structures de Poisson obtenues dans ces limites classiques contiennent différentes algèbres W N q-déformées dépendant de la parité de l'entier h, caractérisant les structures d'´ echangè a p = q N h comme de nouvelles algèbres W q,p (sl(N)).
18478779
A braided Yang–Baxter algebra in a theory of two coupled lattice quantum KdV: algebraic properties and ABA representations
A generalization of the Yang–Baxter algebra is found in quantizing the monodromy matrix of two (m)KdV equations discretized on a space lattice. This braided Yang–Baxter equation still ensures that the transfer matrix generates operators in involution which form the Cartan sub-algebra of the braided quantum group. Representations diagonalizing these operators are described through relying on an easy generalization of algebraic Bethe ansatz techniques. The conjecture that this monodromy matrix algebra leads, in the cylinder continuum limit, to a perturbed minimal conformal field theory description is analysed and supported.
122826165
Non-linear integral equations in N = 4 SYM ∗
We survey and discuss the applications of the non-linear integral equation in the framework of the Bethe Ansatz type equations which are conjectured to give the eigenvalues of the dilatation operator in N = 4 SYM. Moreover, an original idea (different from that of [1]) to derive a non-linear integral equation is briefly depicted in Section 4.
55875652
A Wide Area Electron Beam Scanner
A wide-area electron beam scanner, which utilizes a single three-phase electromagnet has been designed and constructed for use with Grumman's 3 MV Van de Graaff accelerator. The uniformity of the beam scan has been measured, and between radii of 1 and 4? inches has been found to be constant to within ±10 percent (%).