R-matrix and Baxter Q-operators for the noncompact SL(N,C) invariant spin chain

The problem of constructing the SL(N,C) invariant solutions to the Yang-Baxter equation is considered. The solutions (R-operators) for arbitrarily principal series representations of SL(N,C) are obtained in an explicit form. We construct the commutative family of the operators Qk(u) which can be identified with the Baxter operators for the noncompact SL(N,C) spin magnet

Evolution of twist-three parton distributions in QCD beyond the large N_c limit

We formulate a consistent 1/N_c^2 expansion of the QCD evolution equations for the twist-three quark distributions g_2(x,Q^2), h_L(x,Q^2) and e(x,Q^2) based on the interpretation of the evolution as a three-particle quantum-mechanical problem with hermitian Hamiltonian. Each distribution amplitude can be decomposed in contributions of partonic components with DGLAP-type scale dependence. We calculate the 1/N_c^2 corrections to the evolution of the dominant component with the lowest anomalous dimension - the only one that survives in the large-N_c limit - and observe a good agreement with the exact numerical results for N_c=3. The 1/N_c^2 admixture of operators with higher anomalous dimensions is shown to be concentrated at a few lowest partonic components and in general is rather weak.Comment: 14 pages, LaTeX style, 2 figure

The spectrum of the anomalous dimensions of the composite operators in the ϵ\epsilon - expansion in the scalar ϕ4\phi^4 - field theory

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar $\phi^4$ - theory in the first order of the $\epsilon$ -expansion is investigated. The exact solution for the operators with number of fields $\leq 4$ is presented. The behaviour of the anomalous dimensions in the large $l$ limit has been analyzed. It is given the qualitative description of the %structure of the spectrum for the arbitrary $n$.Comment: 25 pages, latex, a few changes in latex command

NNLO anomalous dimension matrix for twist-two flavor-singlet operators

Conformal symmetry of QCD is restored at the Wilson-Fisher critical point in noninteger 4 −2�space-time dimensions. Correlation functions of multiplicatively renormalizable operators with different anomalous dimensions at the critical point vanish identically. We show that this property allows one to calculate off-diagonal parts of the anomalous dimension matrices for leading-twist operators from a set of two-point correlation functions of gauge-invariant operators which can be evaluated using standard computer algebra techniques. As an illustration, we present the results for the NNLO anomalous dimension matrix for flavor-singlet QCD operators for spin N≤8

Evolution equation for the structure function g_2(x,Q^2)

We perform an extensive study of the scale dependence of flavor-singlet contributions to the structure function g_2(x,Q^2) in polarized deep-inelastic scattering. We find that the mixing between quark-antiquark-gluon and three-gluon twist-3 operators only involves the three-gluon operator with the lowest anomalous dimension and is weak in other cases. This means, effectively, that only those three-gluon operators with the lowest anomalous dimension for each moment are important, and allows to formulate a simple two-component parton-like description of g_2(x,Q^2) in analogy with the conventional description of twist-2 parton distributions. The similar simplification was observed earlier for the nonsinglet distributions, although the reason is in our case different.Comment: 53 pages, 10 figures, LaTeX styl

Multi-reggeon compound states and resummed anomalous dimensions in QCD

We perform the OPE analysis of the contribution of colour-singlet compound states of reggeized gluons to a generic hard process in QCD and calculate the spectrum of the corresponding higher twist anomalous dimensions in multi-colour limit. These states govern high energy asymptotics of the structure functions and their energies define the intercept of the Regge singularities both in the Pomeron and the Odderon sectors. We argue that due to nontrivial analytical properties of the energy spectrum, the twist expansion does not hold for the gluonic states with the minimal energy generating the leading Regge singularities. It is restored however after one takes into account the states with larger energies whose contribution to the Regge asymptotics is subleading.Comment: 15 pages, 2 figures. Minor changes, references adde

The simple scheme for the calculation of the anomalous dimensions of composite operators in the 1/N expansion

The simple method for the calculating of the anomalous dimensions of the composite operators up to 1/N^2 order is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the $(\otimes\vec\Phi)^{s}$ and $\vec\Phi\otimes(\otimes\vec\partial)^{n}\vec\Phi$ operators in the 1/N^2 order in the nonlinear sigma model. The special simplifications due to the conformal invariance of the model are discussed.Comment: 20 pages, Latex, uses Feynman.st

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