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.
14982537
On the commuting charges for the highest dimension SU(2) operators in planar = 4 SYM
We consider the highest anomalous dimension operator in the SU(2) sector of planar = 4 SYM at all-loop, though neglecting wrapping contributions. In any case, the latter enter the loop expansion only after a precise length-depending order. In the thermodynamic limit we write both a linear integral equation for the Bethe root density and a linear system obeyed by the commuting charges. Consequently, we determine the leading strong coupling contribution to the density and from this an approximation to the leading and sub-leading terms of any charge Qr: it scales as λ1/4−r/2, which generalises the Gubser-Klebanov-Polyakov energy law. In the end, we briefly extend these considerations to finite lengths and 'excited' operators by using the idea of a non-linear integral equation.
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.
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
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.
118358387
On the scattering over the GKP vacuum
Abstract By converting the asymptotic Bethe Ansatz (ABA) of N = 4 SYM into non-linear integral equations, we find 2D scattering amplitudes of excitations on top of the GKP vacuum. We prove that this is a suitable and powerful set-up for the understanding and computation of the whole S-matrix. We show that all the amplitudes depend on the fundamental scalar–scalar one.
119215247
New Physics at CDF
The Standard Model (SM) of particle interactions is one of the major achievements of fundamental science. However, despite its success in predicting experimental results through the years, several fundamental issues are left open such as: the origin of dark matter in the universe, the existence of a unifying theory of all known forces and interactions, why particles have the masses we observe and the hierarchy problem. Supersymmetry (SUSY) is one of the possible extensions of the SM. It proposes an additional symmetry that predicts the existence of an additional boson (fermion) for each SM fermion (boson). The appeal of SUSY is closely related to the fact that it naturally solves several of the open questions of the SM. Thus it is extensively tested in an experiment as CDF where many of its signatures can be searched for. On the other hand there is still no compelling reason to exclude other scenarios like Extra-dimensions and New Gauge Interaction Models, a priori. The CDF program in physics beyond the SM is quite rich and here we present some representative searches subdivided in two main categories: SUSY and non-SUSY searches. We present the current status of searches for physics beyond the Standard Modelmore » at the Tevatron 1.96-TeV proton-antiproton collider using data collected with the CDF experiment. We cover searches for supersymmetry, extra dimensions and new gauge bosons.« less
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 (%).