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.
15274892
On the Quasi-Hopf Structure of Deformed Double Yangians
We construct universal twists connecting the centrally extended double Yangian DYrm(sl(2))c with deformed double Yangians DYrm(sl(2))c, thereby establishing the quasi-Hopf structures of the latter.
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.
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.
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.
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 (%).