Yang-Baxter operators and scattering amplitudes in N=4\mathcal{N} = 4 super-Yang-Mills theory

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the extended symmetry and to recover as its consequences many known features like cyclic and inversion symmetry, BCFW recursion, Inverse Soft Limit construction, Grassmannian integral representation, $\mathrm{R}$-invariants and on-shell diagram approach.Comment: 32 pages, 10 figures, final version for publicatio

Orthogonal and symplectic Yangians and Yang-Baxter R-operators

Yang-Baxter R operators symmetric with respect to the orthogonal and symplectic algebras are considered in an uniform way. Explicit forms for the spinorial and metaplectic R operators are obtained. L operators, obeying the RLL relation with the orthogonal or symplectic fundamental R matrix, are considered in the interesting cases, where their expansion in inverse powers of the spectral parameter is truncated. Unlike the case of special linear algebra symmetry the truncation results in additional conditions on the Lie algebra generators of which the L operators is built and which can be fulfilled in distinguished representations only. Further, generalised L operators, obeying the modified RLL relation with the fundamental R matrix replaced by the spinorial or metaplectic one, are considered in the particular case of linear dependence on the spectral parameter. It is shown how by fusion with respect to the spinorial or metaplectic representation these first order spinorial L operators reproduce the ordinary L operators with second order truncation.Comment: 24 page

Diffractive meson production from virtual photons with odd charge-parity exchange

We calculate the cross section of diffractive charge-parity C=+1 neutral meson production in virtual photon proton collision at high energies. Due to the opposite C-parities of photon and meson M (M = eta_C, pi^0, a_2) this process probes the t-channel C=-1 odderon exchange which is described here as noninteracting three-gluon exchange. Estimates for the cross section of the inelastic diffractive process gamma^* p -> eta_C X_p are presented. The total cross section of diffractive \eta_C meson photoproduction is found to be 47 pb. The cross sections for the diffractive production of light mesons (pi^0, a_2) in \gamma^* p collisions are of the same order if the photon virtuality Q^2 is m^2_C.Comment: LaTeX, 19 pages, 8 ps-figs, epsfi

Orthogonal and symplectic Yangians: oscillator realization

We solve RLL-relation with fundamental orthogonal/symplectic R-matrix examining polynomial with respect to u expressions for L-operator. We use creation-annihilation operators to construct a realization of Yangian generators