Publications (24)91.59 Total impact
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ABSTRACT: Scattering amplitudes in N = 4 superYang Mills theory can be computed to higher perturbative orders than in any other fourdimensional quantum field theory. The results are interesting transcendental functions. By a hidden symmetry (dual conformal symmetry) the arguments of these functions have a geometric interpretation in terms of configurations of points in CP^3 and they turn out to be cluster coordinates. We briefly introduce cluster algebras and discuss their Poisson structure and the Sklyanin bracket. Finally, we present a 40term trilogarithm identity which was discovered by accident while studying the physical results.  [Show abstract] [Hide abstract]
ABSTRACT: We perform a detailed study of the Yangian symmetry of smooth supersymmetric MaldacenaWilson loops in planar N=4 super YangMills theory. This hidden symmetry extends the global superconformal symmetry present for these observables. A gaugecovariant action of the Yangian generators on the Wilson line is established that generalizes previous constructions built upon path variations. Employing these generators the Yangian symmetry is proven for general paths in nonchiral N=4 superspace at the first perturbative order. The bilocal piece of the levelone generators requires the use of a regulator due to divergences in the coincidence limit. We perform regularization by point splitting in detail, thereby constructing additional local and boundary contributions as regularization for all levelone Yangian generators. Moreover, the Yangian algebra at level one is checked and compatibility with local kappasymmetry is established. Finally, the consistency of the Yangian symmetry is shown to depend on two properties: The vanishing of the dual Coxeter number of the underlying superconformal algebra and the existence of a novel superspace "Gidentity" for the gauge field theory. This tightly constrains the conformal gauge theories to which integrability can possibly apply.  [Show abstract] [Hide abstract]
ABSTRACT: We consider a supersymmetric Wilson loop operator for 4d N = 4 super YangMills theory which is the natural object dual to the AdS 5× S 5 superstring in the AdS/CFT correspondence. It generalizes the traditional bosonic 1/2 BPS MaldacenaWilson loop operator and completes recent constructions in the literature to smooth (nonlightlike) loops in the full \( \mathcal{N}=4 \) nonchiral superspace. This Wilson loop operator enjoys global superconformal and local kappasymmetry of which a detailed discussion is given. Moreover, the finiteness of its vacuum expectation value is proven at leading order in perturbation theory. We determine the leading vacuum expectation value for general paths both at the component field level up to quartic order in anticommuting coordinates and in the full nonchiral superspace in suitable gauges. Finally, we discuss loops built from quadric splines joined in such a way that the path derivatives are continuous at the intersection.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we construct a lightlike polygonal Wilson loop in \( \mathcal{N} \) = 6 superspace for ABJM theory. We then use it to obtain constraints on its two and threeloop bosonic version, by focusing on higher order terms in the θ expansion. The Grassmann expansion of the threeloop answer contains integrals which may be elliptic polylogarithms. Our results take their simplest form when expressed in terms of OSp(64) supertwistors.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we construct a lightlike polygonal Wilson loop in N=6 superspace for ABJM theory. We then use it to obtain constraints on its two and threeloop bosonic version, by focusing on higher order terms in the $\theta$ expansion. The Grassmann expansion of the threeloop answer contains integrals which may be elliptic polylogarithms. Our results take their simplest form when expressed in terms of OSp(64) supertwistors.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper we study motivic amplitudesobjects which contain all of the essential mathematical content of scattering amplitudes in planar SYM theory in a completely canonical way, free from the ambiguities inherent in any attempt to choose particular functional representatives. We find that the cluster structure on the kinematic configuration space Conf_n(P^3) underlies the structure of motivic amplitudes. Specifically, we compute explicitly the coproduct of the twoloop sevenparticle MHV motivic amplitude A_{7,2} and find that like the previously known sixparticle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster Xcoordinates on Conf_n(P^3). We also find intriguing relations between motivic amplitudes and the geometry of generalized associahedrons, to which cluster coordinates have a natural combinatoric connection. For example, the obstruction to A_{7,2} being expressible in terms of classical polylogarithms is most naturally represented by certain quadrilateral faces of the appropriate associahedron. We also find and prove the first known functional equation for the trilogarithm in which all 40 arguments are cluster Xcoordinates of a single algebra. In this respect it is similar to Abel's 5term dilogarithm identity.  [Show abstract] [Hide abstract]
ABSTRACT: We show that the offshell N=3 action of N=4 super YangMills can be written as a holomorphic ChernSimons action whose Dolbeault operator is constructed from a complexreal (CR) structure of harmonic space. We also show that the local spacetime operators can be written as a Penrose transform on the coset SU(3)/(U(1) \times U(1)). We observe a strong similarity to ambitwistor space constructions.  [Show abstract] [Hide abstract]
ABSTRACT: We compute the oneloop expectation value of lightlike polygonal Wilson loops in superYang–Mills theory in full superspace. When projecting to chiral superspace, we recover the known results for the treelevel nexttomaximallyhelicityviolating scattering amplitude. The oneloop maximallyhelicityviolating amplitude is also included in our result but there are additional terms which do not immediately correspond to scattering amplitudes. We finally discuss different regularizations and their Yangian anomalies.  [Show abstract] [Hide abstract]
ABSTRACT: Recent progress on scattering amplitudes has benefited from the mathematical technology of symbols for efficiently handling the types of polylogarithm functions which frequently appear in multiloop computations. The symbol for all twoloop maximally helicity violating amplitudes in planar supersymmetric YangMills theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multiRegge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multiRegge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct BalitskyFadinKuraevLipatov computation carried out in a parallel publication.  [Show abstract] [Hide abstract]
ABSTRACT: We discuss various formulations of null polygons in full, nonchiral N=4 superspace in terms of spacetime, spinor and twistor variables. We also note that null polygons are necessarily fat along fermionic directions, a curious fact which is compensated by suitable equivalence relations in physical theories on this superspace.  [Show abstract] [Hide abstract]
ABSTRACT: We present an integral representation for the parityeven part of the twoloop sixpoint planar nexttomaximally helicityviolating amplitude in terms of Feynman integrals which have simple transformation properties under the dual conformal symmetry. We probe the dual conformal properties of the amplitude numerically, subtracting the known infrared divergences. We find that the subtracted amplitude is invariant under dual conformal transformations, confirming existing conjectures through twoloop order. We also discuss the allloop structure of the sixpoint nexttomaximally helicityviolating amplitude and give a parametrization whose dual conformal invariant building blocks have a simple physical interpretation.  [Show abstract] [Hide abstract]
ABSTRACT: We present an integral representation for the parityeven part of the twoloop sixpoint planar NMHV amplitude in terms of Feynman integrals which have simple transformation properties under the dual conformal symmetry. We probe the dual conformal properties of the amplitude numerically, subtracting the known infrared divergences. We find that the subtracted amplitude is invariant under dual conformal transformations, confirming existing conjectures through twoloop order. We also discuss the allloop structure of the sixpoint NMHV amplitude and give a parametrization whose dual conformal invariant building blocks have a simple physical interpretation.  [Show abstract] [Hide abstract]
ABSTRACT: We present a compact analytic formula for the twoloop sixparticle maximally helicity violating remainder function (equivalently, the twoloop lightlike hexagon Wilson loop) in N=4 supersymmetric YangMills theory in terms of the classical polylogarithm functions Lik with cross ratios of momentum twistor invariants as their arguments. In deriving our formula we rely on results from the theory of motives.  [Show abstract] [Hide abstract]
ABSTRACT: We revisit the computation of the 2loop correction to the energy of a folded spinning string in AdS 5 with an angular momentum J in S 5 in the scaling limit ln S ≫ 1, . This correction gives the third term in the strongcoupling expansion of the generalized scaling function. The computation, using the AdS lightcone gauge approach developed in our previous paper, is done by expanding the AdS 5 × S 5 superstring partition function near the generalized null cusp world surface associated to the spinning string solution. The result corrects and extends the previous conformal gauge result of arXiv:0712.2479 and is found to be in complete agreement with the corresponding terms in the generalized scaling function as obtained from the asymptotic Bethe ansatz in arXiv:0805.4615 (and also partially from the quantum O(6) model and the Bethe ansatz data in arXiv:0809.4952). This provides a highly nontrivial strong coupling comparison of the Bethe ansatz proposal with the quantum AdS 5 × S 5 superstring theory, which goes beyond the leading semiclassical term effectively controlled by the underlying algebraic curve. The 2loop computation we perform involves all the structures in the AdS lightcone gauge superstring action of hepth/0009171 and thus tests its ultraviolet finiteness and, through the agreement with the Bethe ansatz, its quantum integrability. We do most of the computations for a generalized spinning string solution or the corresponding null cusp surface that involves both the orbital momentum and the winding in a large circle of S 5.  [Show abstract] [Hide abstract]
ABSTRACT: We consider the AdS 5 × S 5 superstring in the lightcone gauge adapted to a massless geodesic in AdS 5 in the Poincaré patch. The resulting action has a relatively simple structure which makes it a natural starting point for various perturbative quantum computations. We illustrate the utility of this AdS lightcone gauge action by computing the 1loop and 2loop corrections to the null cusp anomalous dimension reproducing in a much simpler and efficient way earlier results obtained in conformal gauge. This leads to a further insight into the structure of the superstring partition function in nontrivial background. KeywordsField Theories in Lower DimensionsAdSCFT Correspondence  [Show abstract] [Hide abstract]
ABSTRACT: AdS4/CFT3 duality relating IIA string theory on AdS4× 3 to = 6 superconformal ChernSimons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the treelevel worldsheet scattering for strings on AdS4× 3. We compute all bosonic four, five and sixpoint amplitudes in the gaugefixed action and demonstrate the absence of particle production.  [Show abstract] [Hide abstract]
ABSTRACT: We compute the even part of the planar twoloop MHV amplitude in N=4 supersymmetric YangMills theory, for an arbitrary number of external particles. The answer is expressed as a sum of conformal integrals.  [Show abstract] [Hide abstract]
ABSTRACT: We compute the even part of the twoloop sevenpoint planar MHV amplitude in N=4 supersymmetric YangMills theory. We find that the even part is expressed in terms of conformal integrals with simple rational coefficients. We also compute the even part of two alln cuts. An important feature of the result is that no hexagon (or higher polygon) loops appear among the integrals detected by the cuts we computed. We also present a “leg addition rule,” which allows us to express some integral coefficients in the n+1point MHV amplitude in terms of the integral coefficients of the npoint MHV amplitude. 
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ABSTRACT: This thesis is concerned with the study of scattering amplitudes in fourdimensional conformal field theories, more particularly the N=4 superYangMills theory. We study this theory first at tree level by using twistor space techniques and review the twistor string models that were proposed to describe it. Then, we turn to the issue of iteration relations and all loop ansatze for scattering amplitudes. We review the unitarity method for computing scattering amplitudes and discuss the Wilson loopscattering amplitude duality that was inspired by the strongcoupling prescription of Alday and Maldacena for scattering amplitudes. We describe in some detail the computation of a twoloop sixpoint scattering amplitude and its surprising equality to the polygonal Wilson loop.
Publication Stats
806  Citations  
91.59  Total Impact Points  
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Institutions

20122014

ETH Zurich
Zürich, Zurich, Switzerland 
University of California, Santa Barbara
 Kavli Institute for Theoretical Physics
Santa Barbara, California, United States


20092012

Brown University
 Department of Physics
Providence, Rhode Island, United States
