Energy-energy correlations in N=4 SYM

We present a new approach to computing energy-energy correlations in gauge theories that exploits their relation to correlation functions and bypasses the use of scattering amplitudes. We illustrate its power by calculating energy-energy correlations in the maximally supersymmetric Yang-Mills theory (N=4 SYM) in the next-to-leading order approximation.Comment: 5 page

Event shapes in N=4 super-Yang-Mills theory

We study event shapes in N=4 SYM describing the angular distribution of energy and R-charge in the final states created by the simplest half-BPS scalar operator. Applying the approach developed in the companion paper arXiv:1309.0769, we compute these observables using the correlation functions of certain components of the N=4 stress-tensor supermultiplet: the half-BPS operator itself, the R-symmetry current and the stress tensor. We present master formulas for the all-order event shapes as convolutions of the Mellin amplitude defining the correlation function of the half-BPS operators, with a coupling-independent kernel determined by the choice of the observable. We find remarkably simple relations between various event shapes following from N=4 superconformal symmetry. We perform thorough checks at leading order in the weak coupling expansion and show perfect agreement with the conventional calculations based on amplitude techniques. We extend our results to strong coupling using the correlation function of half-BPS operators obtained from the AdS/CFT correspondence.Comment: 52 pages, 6 figures; v2: typos correcte

From correlation functions to event shapes

We present a new approach to computing event shape distributions or, more precisely, charge flow correlations in a generic conformal field theory (CFT). These infrared finite observables are familiar from collider physics studies and describe the angular distribution of global charges in outgoing radiation created from the vacuum by some source. The charge flow correlations can be expressed in terms of Wightman correlation functions in a certain limit. We explain how to compute these quantities starting from their Euclidean analogues by means of a non-trivial analytic continuation which, in the framework of CFT, can elegantly be performed in Mellin space. The relation between the charge flow correlations and Euclidean correlation functions can be reformulated directly in configuration space, bypassing the Mellin representation, as a certain Lorentzian double discontinuity of the correlation function integrated along the cuts. We illustrate the general formalism in N=4 SYM, making use of the well-known results on the four-point correlation function of half-BPS scalar operators. We compute the double scalar flow correlation in N=4 SYM, at weak and strong coupling and show that it agrees with known results obtained by different techniques. One of the remarkable features of the N=4 theory is that the scalar and energy flow correlations are proportional to each other. Imposing natural physical conditions on the energy flow correlations (finiteness, positivity and regularity), we formulate additional constraints on the four-point correlation functions in N=4 SYM that should be valid at any coupling and away from the planar limit.Comment: 40 pages, 1 figure; v2: typos correcte

Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory

In this paper we give all the details of the calculation that we presented in our previous paper ArXiv:0908.0387 where the infrared structure of the MHV gluon amplitudes in the planar limit for ${\cal N}=4$ super Yang-Mills theory was considered in the next-to-leading order of perturbation theory. Explicit cancellation of the infrared divergencies in properly defined inclusive cross-sections is demonstrated first in a toy model example of "conformal QED" and then in the real ${\cal N}=4$ SYM theory. We give the full-length details both for the calculation of the real emission and for the diagrams with splitting in initial and final states. The finite parts for some inclusive differential cross-sections are presented in an analytical form. In general, contrary to the virtual corrections, they do not reveal any simple structure. An example of the finite part containing just the log functions is presented. The dependence of inclusive cross-section on the external scale related to the definition of asymptotic states is discussed.Comment: 49 pages, LATEX, 6 eps figures; Minor changes, Refs adde

Mixed-symmetry tensor conserved currents and AdS/CFT correspondence

We present the full list of conserved currents built of two massless spinor fields in Minkowski space and their derivatives multiplied by Clifford algebra elements. The currents have particular mixed-symmetry type described by Young diagrams with one row and one column of arbitrary lengths and heights. Along with Yukawa-like totally antisymmetric currents the complete set of constructed currents exactly matches the spectrum of AdS mixed-symmetry fields arising in the generalized Flato-Fronsdal theorem for two spinor singletons. As a by-product, we formulate and study general properties of primary fields and conserved currents of mixed-symmetry type.Comment: 17 pages; v2: typos corrected, clarifications and refs added; v3: more explanations and refs added; contribution to the J.Phys.A special volume on "Higher Spin Theories and AdS/CFT" edited by Matthias Gaberdiel and Mikhail Vasilie

The Higher Spin/Vector Model Duality

This paper is mainly a review of the dualities between Vasiliev's higher spin gauge theories in AdS4 and three dimensional large N vector models, with focus on the holographic calculation of correlation functions of higher spin currents. We also present some new results in the computation of parity odd structures in the three point functions in parity violating Vasiliev theories.Comment: 55 pages, 1 figure. Contribution to J. Phys. A special volume on "Higher Spin Theories and AdS/CFT" edited by M. R. Gaberdiel and M. Vasiliev. v2: references adde

T-systems and Y-systems in integrable systems

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov-Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analogue of L-operators in KP hierarchy, Stokes phenomena in 1d Schr\"odinger problem, AdS/CFT correspondence, Toda field equations on discrete space-time, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ans\"atze, quantum transfer matrix method and so forth. This review article is a collection of short reviews on these topics which can be read more or less independently.Comment: 156 pages. Minor corrections including the last paragraph of sec.3.5, eqs.(4.1), (5.28), (9.37) and (13.54). The published version (JPA topical review) also needs these correction

Form factors at strong coupling via a Y-system

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension