34 research outputs found
R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain
The problem of constructing the invariant solutions to the
Yang-Baxter equation is considered. The solutions (-operators) for
arbitrarily principal series representations of are obtained
in an explicit form. We construct the commutative family of the operators
which can be identified with the Baxter operators for the
noncompact spin magnet.Comment: This is a contribution to the Vadim Kuznetsov Memorial Issue on
Integrable Systems and Related Topics, published in SIGMA (Symmetry,
Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
On evolution kernels of twist-two operators
The evolution kernels that govern the scale dependence of the generalized
parton distributions are invariant under transformations of the
collinear subgroup of the conformal group. Beyond
one loop the symmetry generators, due to quantum effects, differ from the
canonical ones. We construct the transformation which brings the {\it full}
symmetry generators back to their canonical form and show that the eigenvalues
(anomalous dimensions) of the new, canonically invariant, evolution kernel
coincide with the so-called parity respecting anomalous dimensions. We develop
an efficient method that allows one to restore an invariant kernel from the
corresponding anomalous dimensions. As an example, the explicit expressions for
NNLO invariant kernels for the twist two flavor-nonsinglet operators in QCD and
for the planar part of the universal anomalous dimension in SYM are
presented.Comment: 12 pages, two figures; The three-loop QCD kernel in electronic form
is given in the ancillary fil
Twist-four Corrections to Parity-Violating Electron-Deuteron Scattering
Parity violating electron-deuteron scattering can potentially provide a clean
access to electroweak couplings that are sensitive to physics beyond the
Standard Model. However hadronic effects can contaminate their extraction from
high-precision measurements. Power-suppressed contributions are one of the main
sources of uncertainties along with charge-symmetry violating effects in
leading-twist parton densities. In this work we calculate the twist-four
correlation functions contributing to the left-right polarization asymmetry
making use of nucleon multiparton light-cone wave functions.Comment: 12 pages, 3 figure
Operator mixing in fermionic CFTs in noninteger dimensions
We consider the renormalization of four-fermion operators in the critical QED and SU(N-c) thorn version of the Gross-Neveu-Yukawa model in noninteger dimensions. Since the number of mixing operators is infinite, the diagonalization of an anomalous dimension matrix becomes a nontrivial problem. At leading order, the construction of eigenoperators is equivalent to solving certain three-term recurrence relations. We find analytic solutions of these recurrence relations that allow us to determine the spectrum of anomalous dimensions and study their properties
Correction exponents in the Gross–Neveu–Yukawa model at 1/N2
We calculate the critical exponents omega +/- in the d-dimensional Gross-Neveu model in 1/N expansion with 1/N-2 accuracy. These exponents are related to the slopes of the ss-functions at the critical point in the Gross-Neveu-Yukawa model. They have been computed recently to four loops accuracy. We checked that our results are in complete agreement with the results of the perturbative calculations
Three-loop off-forward evolution kernel for axial-vector operators in Larin’s scheme
Evolution equations for leading-twist operators in high orders of perturbation theory can be restored from the spectrum of anomalous dimensions and the calculation of the special conformal anomaly at one order less using conformal symmetry of QCD at the Wilson-Fisher critical point at noninteger d=4−2ϵ space-time dimensions. In this work, we generalize this technique to axial-vector operators. We calculate the corresponding three-loop evolution kernels in Larin’s scheme and derive explicit expressions for the finite renormalization kernel that describes the difference to the vector case to restore the conventional modified minimal subtraction scheme. The results are directly applicable to deeply virtual Compton scattering and the transition form factor γ∗γ→π
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
We construct the Baxter Q-operator and the representation of the Separated
Variables (SoV) for the homogeneous open SL(2,R) spin chain. Applying the
diagrammatical approach, we calculate Sklyanin's integration measure in the
separated variables and obtain the solution to the spectral problem for the
model in terms of the eigenvalues of the Q-operator. We show that the
transition kernel to the SoV representation is factorized into the product of
certain operators each depending on a single separated variable. As a
consequence, it has a universal pyramid-like form that has been already
observed for various quantum integrable models such as periodic Toda chain,
closed SL(2,R) and SL(2,C) spin chains.Comment: 29 pages, 9 figures, Latex styl
Separation of variables for the quantum SL(2,R) spin chain
We construct representation of the Separated Variables (SoV) for the quantum
SL(2,R) Heisenberg closed spin chain and obtain the integral representation for
the eigenfunctions of the model. We calculate explicitly the Sklyanin measure
defining the scalar product in the SoV representation and demonstrate that the
language of Feynman diagrams is extremely useful in establishing various
properties of the model. The kernel of the unitary transformation to the SoV
representation is described by the same "pyramid diagram" as appeared before in
the SoV representation for the SL(2,C) spin magnet. We argue that this kernel
is given by the product of the Baxter Q-operators projected onto a special
reference state.Comment: 26 pages, Latex style, 9 figures. References corrected, minor
stylistic changes, version to be publishe
Transversity Form Factors and Generalized Parton Distributions of the pion in chiral quark models
The transversity Generalized Parton Distributions (tGPDs) and related
transversity form factors of the pion are evaluated in chiral quark models,
both local (Nambu--Jona-Lasinio) and nonlocal, involving a momentum-dependent
quark mass. The obtained tGPDs satisfy all a priori formal requirements, such
as the proper support, normalization, and polynomiality. We evaluate
generalized transversity form factors accessible from the recent lattice QCD
calculations. These form factors, after the necessary QCD evolution, agree very
well with the lattice data, confirming the fact that the spontaneously broken
chiral symmetry governs the structure of the pion also in the case of the
transversity observables.Comment: 6 pages, 3 figures, presented by WB at LIGHTCONE 2011, 23 - 27 May,
2011, Dalla