R-Matrix and Baxter Q-Operators for the Noncompact SL(N,C) Invariant Spin Chain

The problem of constructing the $SL(N,\mathbb{C})$ invariant solutions to the Yang-Baxter equation is considered. The solutions ($\mathcal{R}$-operators) for arbitrarily principal series representations of $SL(N,\mathbb{C})$ are obtained in an explicit form. We construct the commutative family of the operators $\mathcal{Q}_k(u)$ which can be identified with the Baxter operators for the noncompact $SL(N,\mathbb{C})$ 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 $\mathrm{SL}(2,\mathrm R)$ 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 $N=4$ 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