We consider correlators of N=4 super Yang Mills of the form A ~ < O_1 O_2 O*_1 O*_2 >, where the operators O_1 and O_2 are scalar primaries. In particular, we analyze this correlator in the planar limit and in a Lorentzian regime corresponding to high energy interactions in AdS. The planar amplitude is dominated by a Regge pole whose nature varies as a function of the 't Hooft coupling g^2. At large g, the pole corresponds to graviton exchange in AdS, whereas at weak g, the pole is that of the hard perturbative BFKL pomeron. We concentrate on the weak coupling regime and analyze pomeron exchange directly in position space. The analysis relies heavily on the conformal symmetry of the transverse space E^2 and of its holographic dual hyperbolic space H_3, describing with an unified language, both the weak and strong 't Hooft coupling regimes. In particular, the form of the impact factors is highly constrained in position space by conformal invariance. Finally, the analysis suggests a possible AdS eikonal resummation of multi-pomeron exchanges implementing AdS unitarity, which differs from the usual 4-dimensional eikonal exponentiation. Relations to violations of 4-dimensional unitarity at high energy and to the onset of nonlinear effects and gluon saturation become immediate questions for future research.
We calculate the interaction vertex of three BFKL states including the bare triple BFKL Pomeron coupling and discuss its relation with the correlation functions in two-dimensional conformal field theory. We construct the operator algebra of the fields interpolating the BFKL states and show that in the multi-color limit the vertex satisfies the constraints imposed by the conformal bootstrap on the structure constants of the operator product expansion in conformal field theory.
Conformally invariant reggeon interactions derived from $t$-channel unitarity are discussed and progress towards understanding the ``physical Pomeron'', via massless quark reggeon interactions, is briefly outlined.
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 physi…
We show that a resummation model for the evolution kernel at small x creates a bridge between the weak and strong couplings. The resummation model embodies DGLAP and BFKL anomalous dimensions at leading logarithmic orders, as well as a kinematical constraint on the real emission part of the kernel. In the case of pure gluodynamics the strong coupling limit of the Pomeron intercept is consistent with the exchange of the spin-two, colorless particle.
In this paper we encode the perturbative BFKL leading logarithmic resummation, relevant for the Regge limit behavior of QCD scattering amplitudes, in the IR-regulated effective action which satisfies exact functional renormalization group equations. This is obtained using a truncation with a specific infinite set of non local vertices describing the multi-Regge kinematics (MRK). The goal is to use this framework to study, in the high energy limit and at larger transverse distances the transition to a much simpler effective local reggeon field theory, whose critical properties were recently inv…
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 $ω$-space for $t=0$ coincides with the continuous spectrum for the massless case although the density of its eigenvalues is two times smaller for $ω>ω_0$, where $ω_0$ is a negative number. We find a simple parametrization for the correspond…
We find the eigenvalue of the kernel of BFKL equation in the next-to-next-to-leading logarithm approximation in the planar N=4 SM theory from the constraints, coming from the six-loop anomalous dimension of twist-2 operators and known large-gamma limit.
We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than 60 digits precision using the numerical method developed by us in a previous paper. As a byproduct we developed a general analytic method of solving the QSC perturbatively.
After a brief review of the BFKL approach to Regge processes in QCD and in supersymmetric (SUSY) gauge theories we propose a strategy for calculating the next-to-next-to-leading order corrections to the BFKL kernel. They can be obtained in terms of various cross-sections for Reggeized gluon interactions. The corresponding amplitudes can be calculated in the framework of the effective action for high energy scattering. In the case of N=4 SUSY it is also possible to use the Bern-Dixon-Smirnov (BDS) ansatz. For this purpose the analytic properties of the BDS amplitudes at high energies are invest…
Imposing infrared boundary conditions on the BFKL equation with running coupling transforms the complex momentum w-plane cut present in the gluon Green function into an infinite series of positive Regge poles. In addition, a cut on the negative w line remains. We consider a Hermitian kernel at leading order with running coupling and construct the gluon Green function performing the w integration away from the real axis. We find a strong dependence of the asymptotic intercepts and collinear behaviour on the non-perturbative choice of the boundary conditions, in the form of an infrared phase. Th…
We find the eigenvalue of the kernel of BFKL equation in the next-to-next-to-next-to-leading logarithm approximation (NNNLLA) in the planar N=4 SYM theory by using the quantum spectral curve to compute values at fixed spin, and reconstructing the general result using the LLL-algorithm, which also was used for the reconstruction of the general result for the intercept function for arbitrary conformal spin at fourth order, computed earlier in paper 1802.06908 up to the rational part. We have found, that a new type of harmonic sums enter into results. Those sums have the argument multiplied by fa…
We identify classical string solutions which directly give the classical part of the strong coupling pomeron intercept. The relevant solution is a close cousin of the GKP folded string, which is not surprising given the known relation with twist-2 operators. Our methods are applicable, however, also for nonzero conformal spin where we do not have a clear link with anomalous dimensions of a concrete class of operators. We analyze the BFKL folded string from the algebraic curve perspective and investigate its possible particle content.
We derive the full analytic expression for the QCD eikonal coupling of a quark-antiquark state to the exchanged gluon-gluon state in the BFKL formalism. The formula is valid for all conformal spin configurations of the quark-antiquark and gluon-gluon states. In particular, a new selection rule on conformal spins characterizes the non-dominant BFKL components with intercept below the Pomeron in the conformal-invariant framework.
We review the theoretical approaches for investigations of the high energy hadron-hadron scattering in the Regge kinematics. It is demonstrated, that the gluon in QCD is reggeized and the Pomeron is a composite state of the reggeized gluons. Remarkable properties of the BFKL equation for the Pomeron wave function in QCD and supersymmetric gauge theories are outlined. Due to the AdS/CFT correspondence the BFKL Pomeron is equivalent to the reggeized graviton in the extended N=4 SUSY. The properties of the maximal transcendentality and integrability are realized in this model. The BDS multi-gluon…
The conformal invariance properties of the QCD Pomeron in the transverse plane allow us to give an explicit analytical expression for the solution of the BFKL equations both in the transverse coordinate and momentum spaces. This result is obtained from the solution of the conformal eigenvectors in the mixed representation in terms of two conformal blocks, each block being the product of an holomorphic times an antiholomorphic function. This property is used to give an exact expression for the QCD dipole multiplicities and dipole-dipole cross-sections in the whole parameter space, proving the e…
We reinterpret the JIMWLK/KLWMIJ evolution equation as the QCD Reggeon field theory (RFT). The basic "quantum Reggeon field" in this theory is the unitary matrix $R$ which represents the single gluon scattering matrix. We discuss the peculiarities of the Hilbert space on which the RFT Hamiltonian acts. We develop a perturbative expansion in the RFT framework, and find several eigenstates of the zeroth order Hamiltonian. The zeroth order of this perturbation preserves the number of $s$ - channel gluons. The eigenstates have a natural interpretation in terms of the $t$ - channel exchanges. Study…
The high-energy behavior of the N=4 SYM amplitudes in the Regge limit can be calculated order by order in perturbation theory using the high-energy operator expansion in Wilson lines. At large $N_c$, a typical four-point amplitude is determined by a single BFKL pomeron. The conformal structure of the four-point amplitude is fixed in terms of two functions: pomeron intercept and the coefficient function in front of the pomeron (the product of two residues). The pomeron intercept is universal while the coefficient function depends on the correlator in question. The intercept is known in the firs…
We consider the QCD scattering amplitudes at high energies sqrt{s} and fixed momentum transfers sqrt{-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 Pomeron wave function for arbitrary T is calculated using an integral of motion. In multi-colour QCD, the holomorphic Hamiltonian for n-reggeized gluons at temperature T is shown to coincide with the local Hamiltonian of an integrable Heisenberg model and can be obtained from the T=0 Hamiltonian by an unitary transform…
The traditional description of high-energy small-angle scattering in QCD has two components -- a soft Pomeron Regge pole for the tensor glueball, and a hard BFKL Pomeron in leading order at weak coupling. On the basis of gauge/string duality, we present a coherent treatment of the Pomeron. In large-N QCD-like theories, we use curved-space string-theory to describe simultaneously both the BFKL regime and the classic Regge regime. The problem reduces to finding the spectrum of a single j-plane Schrodinger operator. For ultraviolet-conformal theories, the spectrum exhibits a set of Regge trajecto…
Using the methods of the recently proposed Quantum Spectral Curve (QSC) originating from integrability of ${\cal N}=4$ Super--Yang-Mills theory we analytically continue the scaling dimensions of twist-2 operators and reproduce the so-called pomeron eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation. Furthermore, we recovered the Faddeev-Korchemsky Baxter equation for Lipatov's spin chain and also found its generalization for the next-to-leading order in the BFKL scaling. Our results provide a non-trivial test of QSC describing the exact spectrum in planar ${\cal N}=4$ SYM at infin…
The holographic approach to double diffractive Higgs production is presented for the AdS graviton/Pomeron. The goal is to provide a predictive phenomenology for the strong coupling expansion of QCD. This is the first step to set up the framework for the double diffractive Higgs production in anticipation of experimental observations at the LHC. Comparisons are made with the weak coupling approach based on the BFKL Pomeron models and soft Regge parameterizations.
We derive the analytic expression of the two one-loop dipole contributions to the elastic 4-gluon amplitude in QCD. The first one corresponds to the double QCD pomeron exchange, the other to an order alpha^2 correction to one-pomeron exchange. Both are expressed in terms of the square of the recently derived triple QCD pomeron vertex and involve a summation over all conformal Eigenvectors of the BFKL kernel.
In the framework of the effective field theory for interacting BFKL pomerons, applied to nucleus-nucleus scattering, boundary conditions for the classical field equations are discussed. Correspondence with the QCD diagrams at the boundary rapidities requires pomeron interaction with the participating nuclei to be exponential and non-local. Commonly used 'eikonal' boundary conditions, local and linear in fields, follow in the limit of small QCD pomeron-nucleon coupling. Numerical solution of the classical field equations, which sum all tree diagrams for central gold-gold scattering, demonstrate…
We begin the process of unitarizing the Pomeron at large 't Hooft coupling. We do so first in the conformal regime, which applies to good accuracy to a number of real and toy problems in QCD. We rewrite the conformal Pomeron in the $J$-plane and transverse position space, and then work out the eikonal approximation to multiple Pomeron exchange. This is done in the context of a more general treatment of the complex $J$-plane and the geometric consequences of conformal invariance. The methods required are direct generalizations of our previous work on single Pomeron exchange and on multiple grav…
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.
We review the result for the BFKL Pomeron intercept at N=4 Supersymmetric Yang-Mills model in the form of the inverse coupling expansion $j_0=2-2λ^{-1/2}-λ^{-1} + 1/4 \, λ^{-3/2} + 2(3ζ_3+1) \, λ^{-2} +(18ζ_3+361/64) \, λ^{-5/2} + (39ζ_3+447/32) \, λ^{-3} + O(λ^{-7/2})$ which has been calculated in [1]-[5] 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.
