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 $f^{(r)}_n(g)$).
119389503
Hubbard's adventures in Script N = 4 SYM-land? Some non-perturbative considerations on finite length operators
As the Hubbard energy at half-filling is believed to reproduce at strong coupling (part of) the all loop expansion of the dimensions in the SU(2) sector of the planar = 4 SYM (super-Yang–Mills theory), we compute an exact non-perturbative expression for it. With this aim, we use the effective and well-known idea in 2D statistical field theory of converting the Bethe ansatz equations into two coupled non-linear integral equations (NLIEs). We focus our attention on the highest anomalous dimension for fixed bare dimension or length, L, analysing the many advantages of this method for extracting exact behaviours on varying the length and the' t Hooft coupling, λ. For instance, we will show that the large L (asymptotic) expansion is exactly reproduced by its analogue in the Beisert–Dippel–Staudacher (BDS) Bethe ansatz, though the exact expression clearly differs from the BDS one (in having non-analytic terms). Taking the limits on L and λ in different orders is also under strict control. Eventually, the precision of numerical integration of the NLIEs is as impressive as in other easier-looking theories.
120678958
Fock representations of exchange algebras with involution
An associative algebra AR with exchange properties generalizing the canonical (anti)commutation relations is considered. We introduce a family of involutions in AR and construct the relative Fock representations, examining the positivity of the metric. As an application of the general results, we rigorously prove unitarity of the scattering operator of integrable models in 1+1 space-time dimensions. In this context the possibility of adopting various involutions in the Zamolodchikov–Faddeev algebra is also explored.
9495374
CENTRAL EXTENSIONS OF CLASSICAL AND QUANTUM Q-VIRASORO ALGEBRAS
We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra Aq,p(sl(N))c. After establishing the expressions of the cocycle conditions, we solve them, both in the classical and in the quantum case (for sl(2)). We find that the consistent central extensions are much more general that those found previously in the literature.
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.
120458416
Unitary group representations in fock spaces with generalized exchange properties
We investigate the notion of secondR-quantization - a suitable deformation of the standard second quantization which properly takes into account the nontrivial exchange properties characterizing generalized statistics. We also perform theR-quantization of a class of unitary one-particle representations relevant for the description of symmetries. The Euclidean covariance of anyons is analyzed within this context.
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 (%).