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The effective action for reggeized gluons is based on the gluodynamic Yang-Mills Lagrangian with external current for longitudinal gluons added, see [1]. On the base of classical solutions, obtained in [2], the one-loop corrections to this effective action in light-cone gauge are calculated. The RFT calculus for reggeized gluons similarly to the RFT introduced in [3] is proposed and discussed. The correctness of the results is verified by calculation of the propagator of $A_{+}$ and $A_{-}$ reggeized gluons fields and application of the obtained results is discussed as well., Comment: 24 pages

Reggeon cuts in QCD amplitudes with negative signature are discussed. These cuts appear in the next-to-next-to-leading logarithmic approximation (NNLLA) and greatly complicate the derivation of the BFKL equation. Feynman diagrams responsible for appearance of these cuts are indicated and the cut contributions are calculated in the two- and three-loop approximation., 13 pages, 4 Figures; some typos corrected, two Figures and some explanations added; results unchanged

The discrete BFKL formalism which accounts for the running of the coupling and incorporates information about the phase of the oscillations at small transverse momentum, arising from the infrared properties of QCD, leads to a QCD pomeron consisting of a set of discrete Regge poles. Here we discuss under what circumstances this discrete pomeron leads to an amplitude which matched the prediction of a DGLAP analysis in the double leading logarithm limit.

We analyse, in NLO, the physical properties of the discrete eigenvalue solution for the BFKL equation. We show that a set of eigenfunctions with positive eigenvalues, \omega, together with a small contribution from a continuum of eigenfunctions with negative \omega, provide an excellent description of high-precision HERA F_2 data in the region, x 6 GeV^2. The phases of the eigenfunctions can be obtained from a simple parametrisation of the pomeron spectrum, which has a natural motivation within BFKL. The data analysis shows that the first eigenfunction decouples completely or almost completely from the proton. This suggests that there exist an additional ground state, which is naturally saturated and may have the properties of the soft pomeron., Comment: 35 pages, 16 figures, the new version gives more explanations of the method and of the results

We consider the BFKL and BKP equations in the leading and next-to-leading approximations in QCD and in N = 4 SUSY. In QCD the spectrum of the Pomeron singularities of the t-channel partial waves is discreet. The BKP equation in LLA is integrable. The effective action for the reggeized gluons gives a possibility to calculate the next-to-leading corrections to the gluon Regge trajectory and Reggeon couplings. We discuss the Mobius invariance of the integral kernels of the BFKL and BKP equations in the next-to-leading order for the color singlet and adjoint representations. In the N = 4 SUSY the BFKL intercept can be calculated in the strong coupling expansion due to the AdS/CFT correspondence. We discuss also the generalization of the effective action approach to the gravity and supergravity. In these models the gravito-graviton scattering amplitude is calculated in the double-logarithmic approximation.

We show the result for the BFKL Pomeron intercept at N = 4 SYM in the form of the inverse coupling expansion j0 = 2 − 2λ−1/2 − λ−1 + 1/4λ−3/2 + 2(1 + 3ζ3)λ−2 + O(λ−5/2), which has been calculated in [1] with the use of the AdS/CFT correspondence.

We find the BFKL Pomeron intercept at N=4 supersymmetric gauge theory in the form of the inverse coupling expansion j0=2-2/lambda**(1/2)-1/lambda + 1/4 1/lambda**(3/2) + 2(1+3zeta3)/lambda**(2) + O(1/lambda**(5/2)) with the use of the AdS/CFT correspondence in terms of string energies calculated recently. The corresponding slope gamma'(2) of the anomalous dimension calculated directly up to the fifth order of perturbation theory turns out to be in an agreement with the closed expression obtained from the recent Basso results., 18 pages, 1 figure, fixed some typos

We review the Balitsky-Fadin-Kuraev-Lipatov approach to high-energy scattering in QCD and supersymmetric gauge theories. At a large number of colors, the equations for the gluon composite states in the t-channel have remarkable mathematical properties including their Mobius invariance, holomorphic separability, duality symmetry, and integrability. We formulate a theory of Reggeized gluon interactions in the form of a gauge-invariant effective action local in particle rapidities. In the maximally extended N=4 supersymmetry, the Pomeron is dual to the Reggeized graviton in the ten-dimensional anti-de Sitter space. As a result, the Gribov Pomeron calculus should be reformulated here as a generally covariant effective field theory for the Reggeized gravitons. We construct the corresponding effective action, which allows calculating the graviton Regge trajectory and its couplings. We sum the double-logarithmic contributions for amplitudes with graviton quantum numbers in the t-channel in the Einstein-Hilbert gravity and its supersymmetric generalizations. As the supergravity rank N increases, the double-logarithmic amplitudes begin to decrease rapidly compared with their Born contributions.

We consider scattering amplitudes in QCD at high energies \(\sqrt s \) and fixed momentum transfers \(q = \sqrt { - t} \) with a non-zero temperature T in the t-channel. In the s-channel the temperature leads to a compactification of the impact parameter plane. We find that the thermal BFKL Hamiltonian in the leading logarithmic approximation proceeds to have the property of the holomorphic separability. Moreover, there exists an integral of motion allowing one to construct the Pomeron wave function for arbitrary T in the coordinate and momentum representations. The holomorphic Hamiltonian for n-reggeized gluons at T ≠ 0 in the multicolour limit Nc → ∞ turns out to be equal to the local Hamiltonian for an integrable Heisenberg spin model. Further, the two-gluon Baxter function coincides with the corresponding wave function in the momentum representation. We calculate the spectrum of the Pomeron Regge trajectories at a finite temperature with taking into account the QCD running coupling. The important effect of the t-channel temperature is the appearence of a confining potential between gluons.

In this paper we proceed with the study of the Pomeron spectrum, by solving numerically the BFKL equation with massive gluons and running coupling. The spectrum of Regge singularities is discrete and the leading Pomeron has a considerable dependence on nonperturbative effects, for which we use Higgs mechanism as a model. We cross-checked this result with variational method and confirmed the infrared sensitivity of leading Pomeron. This fact is related to the infrared instability of the BFKL equation in QCD, with a running coupling. The subleading poles have a mild sensitivity to the soft physics, and are well described by known semiclassical methods. We also discuss the dependence on various prescriptions of the running coupling arguments., 21 pages, 11 Figures

It is known, that the Gribov approach to the hadron-hadron high energy scattering is based on an effective field theory for the Pomeron interactions. The gluons and gravitons are reggeized and therefore it is natural to reformulate QCD and gravity at high energies in terms of the reggeons and their interactions. We review the basic ideas of the BFKL approach in QCD and in supersymmetric gauge models and present it in the form of the gauge-invariant effective theory for the reggeized gluon interactions. A similar generally covariant action for the reggeized gravitons is formulated in terms of effective currents satisfying the Hamilton-Jacobi equation. Its supersymmetric generalization is discussed.

We consider the Gribov approach to hadron-hadron high-energy scattering, which is based on an effective field theory for the Pomeron interactions. Because the gluons and gravitons in QCD and in gravity are Reggeized, it seems natural to reformulate these theories at high energies in terms of Reggeons. We review the basic ideas of the BFKL approach in QCD and in supersymmetric models and present it in the form of a gauge-invariant effective theory for the Reggeized gluon interactions. We formulate the analogous generally covariant action for the Reggeized gravitons in terms of effective currents satisfying the Hamilton-Jacobi equation.

I this talk I discuss the new HERA data on the structure function F2 obtained from a combination of H1 and ZEUS results. Their high precision allows to determine the infrared behaviour of the BFKL forward amplitude for gluon–gluon scattering. This amplitude leads to an excellent description of the new data at low values of x (

We review the BFKL approach based on the use of the analyticity and unitarity for high energy production amplitudes in the multi-Regge kinematics for final states particles. In particular, the Pomeron is a composite state of reggeized gluons. The BFKL dynamics turns out to be integrable at large N c . In N = 4 SUSY the Pomeron is equivalent to a reggeized graviton. We show, that the production amplitudes suggested by Bern, Dixon and Smirnov for this model do not contain the Mandelstam cuts. It turns out, that the corresponding composite states are described by the hamiltonian of an integrable open Heisenberg spin chain.

We present results for the universal anomalous dimension γuni(j) of Wilson twist-2 operators in the \( \mathcal{N} \) = 4 supersymmetric Yang-Mills theory in the first four orders of perturbation theory.

We investigate the Eden-Staudacher and Beisert-Eden-Staudacher equations for the anomalous dimension of twist-2 operators at a large spin s in the \(\mathcal{N} = 4\) supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions ζ(k) having the maximum transcendentality property. We also show that at a large coupling, the “singular” solution of the Beisert-Eden-Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT correspondence.

We investigate the Eden–Staudacher equation for the anomalous dimension of the twist-2 operators at the large spin s in the N = 4 super-symmetric gauge theory. This equation is reduced to a set of linear algebraic equations with the kernel calculated analytically. We prove that in perturbation theory the anomalous dimension is a sum of products of the Euler functions ζ ( k ) having the property of the maximal transcendentality with the coefficients being integer numbers. The radius of convergency of the perturbation theory is found. It is shown, that at g = ∞ the kernel has an essential singularity. The analytic properties of the solution of the Eden–Staudacher equation are investigated. In particular for the case of the strong coupling constant the solution has an essential singularity on the second sheet of the variable j appearing in its Laplace transformation. Similar results are derived also for the Beisert–Eden–Staudacher equation which includes the contribution from the phase related to the crossing symmetry of the underlying S-matrix. We show, that its singular solution at large coupling constants reproduces the anomalous dimension predicted from the string side of the AdS/CFT correspondence.

We present results for the universal anomalous dimension γun(j) of Wilson twist-2 operators in the % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0de9vqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFneVtcqGH9aqpcaaI% 0aaaaa!42BD! $$\mathcal{N} = 4$$ supersymmetric Yang-Mills theory in the first three orders of the perturbation theory. We obtain these expressions by extracting the most complicated terms from the corresponding anomalous dimensions in QCD. The result obtained agrees with the hypothesis of the integrability of the % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0de9vqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWefv3ySLgznf% gDOfdaryqr1ngBPrginfgDObYtUvgaiuaacqWFneVtcqGH9aqpcaaI% 0aaaaa!42BD! $$\mathcal{N} = 4$$ supersymmetric Yang-Mills theory in the context of the AdS/CFT correspondence.

We consider small--angle electron--positron scattering in Quantum Electrodynamics. Leading logarithmic contributions to the cross--section are explicitly calculated to three loop. Next--to--leading terms are exactly computed to two loop. All the radiative corrections due to photons as well as pair production are taken into account. The impact of newly evaluated next-to-leading and higher order leading corrections is discussed and numerical results are explicitly given. The results obtained are generally valid for high and low energy $e^+e^-$ colliders. At LEP and SLC these results can be used to reduce the uncertainty on the cross--section below the per mille level. PACS numbers 12.15.Lk, 12.20.--m, 12.20.Ds, 13.40.--f, Comment: 11 pages, Latex file epsfig.sty with 3 PostScript figures

We describe the (universal) Green function for the discrete BFKL pomeron with running coupling and infrared boundary conditions and discuss the significance of the discrete poles in the case of Deep Inelastic Scattering.

It is shown that the BFKL equation is invariant under a gauge-type transformation. As a result one can impose on the Pomeron wave function Ψ ( ρ → 1 , ρ → 2 ) the colour transparency condition Ψ ( ρ → , ρ → ) = 0 valid for functions in the Mobius representation. The triple Pomeron vertex in the multi-colour QCD at this representation is equivalent to the integral kernel in the Balitiski-Kovchegov (BK) equation. As a result, the BK equation for the dipole density is obtained from the nonlinear equation for the sum of fan diagrams.

We investigate consequences of the M\"obius invariance of the BFKL Hamiltonian and of the triple Pomeron vertex. In particular, we show that the triple Pomeron vertex in QCD, when restricted to the large $N_c$ limit and to the space of M\"obius functions, simplifies and reduces to the vertex used in the Balitsky-Kovchegov (BK) equation. As a result, the BK equation for the dipole density appears as a special case of the nonlinear evolution equation which sums the fan diagrams for BFKL Green's functions in the M\"obius representation. We also calculate the corrections $O(1/(N_c^2-1)$ to the triple Pomeron vertex in the space of M\"obius functions, and we present a generalization of the BK-equation in the next-to-leading order approximation in the $1/N_c$ expansion., Comment: 19 pages, 1 figure

We investigate the Balitsky–Kovchegov (BK) equation for D = 3 space–time dimensions, corresponding to one transverse coordinate, and we show that it can be solved analytically. The explicit solutions are found in the linear approximation and for the particular cases when they do not depend on the impact parameter of the dipole or on its rapidity. It is shown, that in a general case different solutions are related by an infinite parameter group of transformations. The key observation is that the equation has the Kowalewskaya–Painleve property, which gives the possibility of reducing the non-linear problem to the solution of a linear integral equation.

We present results for the three-loop universal anomalous dimension of Wilson twist-2 operators in the N=4 Supersymmetric Yang-Mills model. These results are obtained by extracting the most complicated contributions from the three loop non-singlet anomalous dimensions in QCD which were calculated recently. Their singularities at j=1 agree with the predictions obtained from the BFKL equation for N=4 SYM in the next-to-leading order. The asymptotics of universal anomalous dimension at large j is in an agreement with the expectations based on an interpolation between weak and strong coupling regimes in the framework of the AdS/CFT correspondence., Comment: LaTeX file, 13 pages, no figures. Some corrections, additional remarks and references. In the last version the analysis of anomalous dimension at j -> 2 was improved

It is shown that the interaction of reggeized gluons in the leading logarithmic approximation (LLA) of the multicolor QCD has a number of remarkable mathematical properties, including its conformal invariance, holomorphic factorization, and duality symmetry. The Reggeon Hamiltonian coincides with the Hamiltonian of the integrable Heisenberg model with the spins being the Mobius group generators. Using the Baxter–Sklyanin representation, we calculate intercepts of the colorless states constructed from three and four reggeized gluons and anomalous dimensions of the corresponding higher twist operators. To understand the origin of the integrability of high-energy dynamics in the multicolor QCD in the LLA, we investigate next-to-leading corrections to the BFKL and DGLAP equations in the N = 4 supersymmetric gauge theory beyond the LLA.

The leading logarithmic approximation (LLA) for the scattering amplitudes in QCD is reviewed. The double-logarithmic asymptotics of scattering amplitudes is obtained as a solution to nonlinear evolution equations in the infrared cutoff. The DGLAP equation describes an evolution of parton distributions with increasing parton virtuality. The evolution of the amplitudes with respect to the scale in the longitudinal subspace is given by the BFKL equation. The gluon and quarks in QCD lie on the Regge trajectories calculable in perturbation theory. Mesons and baryons are composite states of Reggeized quarks. Similarly the Pomeron and Odderon are colorless ground states of Reggeized gluons. In the case of multicolor QCD, the Reggeon field theory in LLA is completely integrable. The Reggeon interactions in QCD are derived from a gauge-invariant effective action. In particular, next-to-leading corrections to the BFKL equation in QCD and in supersymmetric gauge models are obtained in this way.

We derive the DGLAP and BFKL evolution equations in the N =4 supersymmetric gauge theory in the next-to-leading approximation. The eigenvalue of the BFKL kernel in this model turns out to be an analytic function of the conformal spin | n |. Its analytic continuation to negative | n | in the leading logarithmic approximation allows us to obtain residues of anomalous dimensions γ of twist-2 operators in the non-physical points j =0,−1,… from the BFKL equation in an agreement with their direct calculation from the DGLAP equation. Moreover, in the multi-color limit of the N =4 model the BFKL and DGLAP dynamics in the leading logarithmic approximation is integrable for an arbitrary number of particles. In the next-to-leading approximation the holomorphic separability of the pomeron Hamiltonian is violated, but the corresponding Bethe–Salpeter kernel has the property of a Hermitian separability. The main singularities of anomalous dimensions γ at j =− r obtained from the BFKL and DGLAP equations in the next-to-leading approximation coincide but our accuracy is not enough to verify an agreement for residues of subleading poles.

We investigate the analytic structure of the $2\ensuremath{\rightarrow}5$ production amplitude in the planar limit of $\mathcal{N}=4$ SYM in the multi-Regge kinematics in all physical regions. We demonstrate the close connection between Regge pole and Regge cut contributions: in a selected class of kinematic regions (Mandelstam regions), the usual factorizing Regge pole formula develops unphysical singularities that have to be absorbed and compensated by Regge cut contributions. This leads, in the corrections to the Bern-Dixon-Smirnov formula, to conformal invariant ``renormalized'' Regge pole expressions in the remainder function. We compute these renormalized Regge poles for the $2\ensuremath{\rightarrow}5$ production amplitude.

We show the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion j0=2-2 lambda**(-1/2)- lambda**(-1) + 1/4 lambda**(-3/2) + 2(1+3zeta3) lambda**(-2) + O(lambda**(-5/2)), which has been calculated recently in [1] with the use of the AdS/CFT correspondence., Comment: 5 pages, talk given at International Moscow Phenomenology Workshop (devoted to the memory of Prof. Alexei Kaidalov), July 21-25, 2013, Moscow, Russia

We solve the BFKL equation in the leading logarithmic approximation numerically in the Yang-Mills theory with the Higgs mechanism for the vector boson mass generation. It can be considered as a model for the amplitude with the correct behavior of the $s$-channel partial waves at large impact parameters. The Pomeron spectrum of the massive BFKL kernel in the $\omega$-space for $t=0$ coincides with the continuous spectrum for the massless case although the density of its eigenvalues is two times smaller for $\omega >\omega _0$, where $\omega_0$ is a negative number. We find a simple parametrization for the corresponding eigenfunctions. Because the leading singularity in the $\omega$-plane in this Higgs model for $t=0$ is a fixed cut, the Regge pole contributions could be only for non-physical positive $t$. Hence we can state that the correct behaviour at large $b$ does not influence the main properties of the BFKL equation., Comment: 35 pages, 21 figures

The next-to-leading corrections to the BFKL equations in QCD and in supersymmetric gauge theories are discussed. In the extended N=4 SUSY they are significantly simplfied, which gives a possibility to relate the BFKL and DGLAP equations in this theory. The gauge-invariant action for the interaction of the reggeized quarks and gluons with the usual partons is constructed and its application to the calculation of the quark Regge trajectory is discussed.

The duality symmetry of the hamiltonian and integrals of motion for reggeon interactions in the multi-colour QCD is formulated as an integral equation for the wave function of compound states of reggeized gluons, which together with the property of holomorphic factorization allows one to reduce the Odderon problem in QCD to the solution of the one-dimensional Schroedinger equation.

We present the differential cross-section for the two-gluon production at high energy collisions in terms of the cross-section for Reggeon-Reggeon → gluon-gluon transitions integrated over the invariant mass of the Reggeons and calculate the corresponding next-to-leading contribution to the kernel of the BFKL equation using the dimensional regularization.

We consider the QCD scattering amplitudes at high energies s and fixed momentum transfers − t in the leading logarithmic approximation at a non-zero temperature T in the t -channel. It is shown that the BFKL Hamiltonian has the property of holomorphic separability. The holomorphic Hamiltonian for n reggeized gluons at temperature T is shown to be obtained from the T = 0 Hamiltonian by an unitary transformation. The connection with field quantization in accelerated frames and black hole backgrounds is discussed.

It is shown that in the next-to-leading approximation of N=4 SUSY the BFKL equation for two-gluon composite states in the adjoint representation of the gauge group can be reduced to a form which is invariant under Moebius transformation in the momentum space. The corresponding similarity transformation of its integral kernel is constructed in an explicit way., Comment: 14 pages

Physics of particles and nuclei 44(3), 547 - 567 (2013). doi:10.1134/S1063779613030052, We analyze, in leading and next to leading order of BFKL, a possible influence of Beyond the Standard Model (BSM) effects on the structure of the discrete pomeron states. We show that the eigenvalues of the states which contribute significantly to the gluon density in the observable region are substantially modified by BSM effects irrespective of the assumptions about the infrared boundary conditions. We also develop a physically motivated heuristic model of the infrared boundary condition which determines the gluon structure function and argue, using this model, that the analysis of the present and future low-$x$ data could allow the detection of a supersymmetry scale in the multi-TeV range. arXiv Springer We analyze, in leading and next to leading order of the BFKL equation, the effects of the quantization of the singularities of the j-plane, t-channel partial waves due to the imposition of appropriate infrared and ultraviolet boundary conditions. We show that the intercepts, ω( )n( ) of the Regge poles, which contribute significantly to the gluon density in the kinematic region measured at HERA and which can be calculated in QCD and in a supersymmetric extension of QCD, are substantially modified by Beyond the Standard Model (BSM) effects. We also develop a physically motivated heuristic model for the infrared boundary condition and apply it to the gluon density. We argue that, using this type of model, the analysis of present and future low-x data could allow one to detect supersymmetry at a high energy scale., Published by MAIK Nauka/Interperiodica, Moskva

In QCD the gluon is reggeized. The Pomeron is a composite state of two reggeized gluons. Its wave function satisfies the BFKL equation. The BFKL Hamiltonian in LLA is invariant under the Mobius transformations. The wave function of the Odderon and other multi-gluon composite states satisfies the BKP equation. The corresponding Hamiltonian in the multi-color limit has the properties of the Mobius invariance, holomorphic separability, duality and integrability. We discuss various approaches applied to the solution of the BKP equation for the singlet and adjoint representations of the gauge group.

We show, that in the leading logarithmic approximation the gluon is reggeized and the pomeron is a compound state of two reggeized gluons. The remarkable properties of the Schrodinger equation for compound states of an arbitrary number of reggeized gluons in the multi-colour QCD are reviewed. The gauge-invariant effective action describing the gluon-Reggeon interactions is constructed. The known next-to-leading corrections to the QCD pomeron are discussed.

We present results for the NLO kernel of the BKP equations for composite states of three reggeized gluons in the Odderon channel, both in QCD and in N=4 SYM. The NLO kernel consists of the NLO BFKL kernel in the color octet representation and the connected $3\to3$ kernel, computed in the tree approximation., 28 pages, 7 figures

We study maximally helicity violating amplitude for the $2\ensuremath{\rightarrow}5$ scattering in the multi-Regge kinematics. The Mandelstam cut correction to the Bern-Dixon-Smirnov amplitude is calculated in the leading logarithmic approximation and the corresponding remainder function is given to any loop order in a closed integral form. We show that the leading logarithmic approximation remainder function at two loops for $2\ensuremath{\rightarrow}5$ amplitude can be written as a sum of two $2\ensuremath{\rightarrow}4$ remainder functions due to recursive properties of the leading order impact factors. We also make some generalizations for the maximally helicity violating amplitudes with more external particles. The results of the present study are in agreement with the all leg two-loop symbol derived by Caron-Huot as shown in a parallel paper of one of the authors with collaborators.

We study the interplay between graviton reggeization and double-logarithmic in energy contributions to four-graviton scattering in theories with and without supersymmetry. Predictions to all orders in the gravitational coupling are given for these double-logarithms. As the number of supersymmetries grows these terms generate a convergent behaviour for the amplitudes at very high energies. At two-loop level, we find agreement with previous exact results for N=8 supergravity and with those of Boucher-Veronneau and Dixon, who studied the N=4,5,6 supergravities using a conjectured double-copy structure of gravity. We study the interplay between graviton reggeization and double-logarithmic in energy contributions to four-graviton scattering in theories with and without supersymmetry. Predictions to all orders in the gravitational coupling are given for these double-logarithms. As the number of supersymmetries grows these terms generate a convergent behaviour for the amplitudes at very high energies. At two-loop level, we find agreement with previous exact results for N=8 supergravity and with those of Boucher-Veronneau and Dixon, who studied the N=4,5,6 supergravities using a conjectured double-copy structure of gravity.

We consider the multi-Regge limit for N=4 SYM NMHV leading color amplitudes in two different formulations: the BFKL formalism for multi-Regge amplitudes in leading logarithm approximation, and superconformal N=4 SYM amplitudes. It is shown that the two approaches agree to two-loops for the 2->4 and 3->3 six-point amplitudes. Predictions are made for the multi-Regge limit of three loop 2->4 and 3->3 NMHV amplitudes, as well as a particular sub-set of two loop 2 ->2 +n N^kMHV amplitudes in the multi-Regge limit in the leading logarithm approximation from the BFKL point of view., 28 pages, 3 figures

Starting from the effective action of high energy QCD we derive Ward identities for Green's functions of reggeized gluons. They follow from the gauge invariance of the effective action, and allow to derive new representations of amplitudes containing physical particles as well as reggeized gluons. We explicitly demonstrate their validity for the BFKL kernel, and we present a new derivation of the kernel., 20 pages, latex, 3 figures

We construct the effective Lagrangian describing QCD in the multi-Regge kinematics. It is obtained from the original QCD Lagrangian by eliminating modes of gluon and quark fields not appearing in this underlying kinematics., 16 pages Latex, 2 figures using package Feynman

We construct, in the framework of QCD, the conformally invariant functional whose maximal value gives theJ-plane location of the leading singularity of thet-channel partial waves in LLA for diagrams withn reggeized gluons. In the case of the odderon the wave function in the impact-parameter space depends on only one anharmonic ratio and the corresponding functional is significantly simplified. By using a variational method with conformal techniques we show that the odderonJ-plane singularity in the LLA approximation of QCD lies above 1.

We consider the planar MHV amplitude in N=4 supersymmetric Yang-Mills theory for 2 -> 4 particle scattering at two and three loops in the Regge kinematics. We perform an analytic continuation of two-loop result for the remainder function found by Goncharov, Spradlin, Vergu and Volovich to the physical region, where the remainder function does not vanish in the Regge limit. After the continuation both the leading and the subleading in the logarithm of the energy terms are extracted and analyzed. Using this result we calculate the next-to-leading corrections to the impact factors required in the BFKL approach. The BFKL technique was used to find the leading imaginary and real parts of the remainder function at three loops.