Alexander Manashov

Quantum integrability in (super) Yang–Mills theory on the light-cone

Abstract We employ the light-cone formalism to construct in the (super) Yang–Mills theories in the multi-color limit the one-loop dilatation operator acting on single trace products of chiral superfields separated by light-like distances. In the N =4 Yang–Mills theory it exhausts all Wilson operators of the maximal Lorentz spin while in nonsupersymmetric Yang–Mills theory it is restricted to the sector of maximal helicity gluonic operators. We show that the dilatation operator in all N -extended super-Yang–Mills theories is given by the same integral operator which acts on the ( N +1) -dimensional superspace and is invariant under the SL(2| N ) superconformal transformations. We construct the R -matrix on this space and identify the dilatation operator as the Hamiltonian of the Heisenberg SL(2| N ) spin chain.

Scale dependence of twist-three contributions to single spin asymmetries

We reexamine the scale dependence of twist-three correlation functions relevant for the single transverse spin asymmetry in the framework of collinear factorization. Evolution equations are derived for both the flavor-nonsinglet and flavor-singlet distributions and arbitrary parton momenta. Our results do not agree with the recent calculations of the evolution in the limit of vanishing gluon momentum. Possible sources for this discrepancy are identified.

Renormalization of twist-four operators in QCD

Extending the work by Bukhvostov, Frolov, Lipatov and Kuraev (BFLK) on the renormalization of quasipartonic operators we derive a complete set of two-particle renormalization group kernels that enter QCD evolution equations to twist-four accuracy. To this end we develop a new technique which essentially bypasses calculation of Feynman diagrams. It is shown that the 2→2 evolution kernels which involve “non-partonic” components of field operators, and, most remarkably, also 2→3 kernels do not require independent calculation and can be restored from the known results for quasipartonic operators using conformal symmetry and Lorentz transformations. The kernels are presented for the renormalization of light-ray operators built of chiral fields in a particular basis such that the conformal symmetry is manifest. The results can easily be recast in momentum space, in the form of evolution equations for generalized parton distributions.

Quantum mechanics of null polygonal Wilson loops

Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of multiparticle GKP excitations. They were shown to emerge from the spectral problem of an underlying open spin chain. In this work we solve this model with the help of the Baxter Q-operator and Sklyanins Separation of Variables methods. We provide an explicit construction for eigenfunctions and eigenvalues of GKP excitations. We demonstrate how the former define the so-called multiparticle hexagon transitions in super-Wison loops and prove their factorized form suggested earlier.

Baryon operators of higher twist in QCD and nucleon distribution amplitudes

We develop a general theoretical framework for the description of higher-twist baryon operators which makes maximal use of the conformal symmetry of the QCD Lagrangian. The conformal operator basis is constructed for all twists. The complete analysis of the one-loop renormalization of twist-4 operators is given. The evolution equation for three-quark operators of the same chirality turns out to be completely integrable. The spectrum of anomalous dimensions coincides in this case with the energy spectrum of the twist-4 subsector of the SU(2,2) Heisenberg spin chain. The results are applied to give a general classification and calculate the scale dependence of subleading twist-4 nucleon distribution amplitudes that are relevant for hard exclusive reactions involving a helicity flip. In particular we find an all-order expression (in conformal spin) for the contributions of geometric twist-3 operators to the (light-cone) twist-4 nucleon distribution amplitudes, which are usually referred to as Wandzura–Wilczek terms.

Superconformal operators in Yang-Mills theories on the light-cone

We employ the light-cone superspace formalism to develop an efficient approach to constructing superconformal operators of twist two in Yang-Mills theories with N=1,2,4 supercharges. These operators have an autonomous scale dependence to one-loop order and determine the eigenfunctions of the dilatation operator in the underlying gauge theory. We demonstrate that for arbitrary N the superconformal operators are given by remarkably simple, universal expressions involving the light-cone superfields. When written in components field, they coincide with the known results obtained by conventional techniques.

Evolution of twist-three parton distributions in QCD beyond the large-Nc 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.Abstract We formulate a consistent 1/Nc2 expansion of the QCD evolution equations for the twist-three quark distributions g2(x,Q2), hL(x,Q2) and e(x,Q2) 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/Nc2 corrections to the evolution of the dominant component with the lowest anomalous dimension – the only one that survives in the large-Nc limit – and observe a good agreement with the exact numerical results for Nc=3. The 1/Nc2 admixture of operators with higher anomalous dimensions is shown to be concentrated at a few lowest partonic components and in general is rather weak.

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

A simple method for the calculation of the anomalous dimensions of composite operators up to order 1/N2 is developed. We demonstrate the effectiveness of this approach by computing the critical exponents of the (⊗φ)s and (φ ⊗ (⊗∂)nφ) operators to order 1/N2 in the non-linear σ-model. The special simplifications due to the conformal invariance of the model are discussed.

Finite-tand target mass corrections to deeply virtual Compton scattering on a scalar target

Using the formalism developed in [1, 2] we carry out the first complete calculation of kinematic power corrections to the helicity amplitudes of deeply-virtual Compton scattering to the twist-four accuracy for a study case of a (pseudo)scalar target. Our main result is that both finite–t, ∼ t/Q, and target mass, ∼ m/Q, twist-four kinematic power corrections turn out to be factorizable, at least to the leading order in the strong coupling. The structure of these corrections is discussed and a short model study of their numerical impact is presented.

Integrability of the evolution equations for heavy–light baryon distribution amplitudes

We consider evolution equations describing the scale dependence of the wave function of a baryon containing an infinitely heavy quark and a pair of light quarks at small transverse separations, which is the QCD analogue of the helium atom. The evolution equations depend on the relative helicity of the light quarks. For the aligned helicities, we find that the equation is completely integrable, that is, it has a nontrivial integral of motion, and obtain exact analytic expressions for the eigenfunctions and the anomalous dimensions. The evolution equation for anti-aligned helicities contains an extra term that breaks integrability and creates a “bound state” with the anomalous dimension separated from the rest of the spectrum by a finite gap. The corresponding eigenfunction is found using numerical methods. It describes the momentum fraction distribution of the light quarks in, e.g., Λb-baryon at large scales.