C. Vergu

Hochschule für Technik Zürich, Zürich, Zurich, Switzerland

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Publications (14)32.18 Total impact

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    ABSTRACT: In this paper we study motivic amplitudes--objects 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 two-loop seven-particle MHV motivic amplitude A_{7,2} and find that like the previously known six-particle amplitude, it depends only on certain preferred coordinates known in the mathematics literature as cluster X-coordinates 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 X-coordinates of a single algebra. In this respect it is similar to Abel's 5-term dilogarithm identity.
    05/2013;
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    Burkhard U. W. Schwab, Cristian Vergu
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    ABSTRACT: We show that the off-shell N=3 action of N=4 super Yang-Mills can be written as a holomorphic Chern-Simons action whose Dolbeault operator is constructed from a complex-real (CR) structure of harmonic space. We also show that the local space-time 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.
    Journal of High Energy Physics 01/2013; 2013(3). · 5.62 Impact Factor
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    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 two-loop maximally helicity violating amplitudes in planar supersymmetric Yang-Mills theory is known, but explicit analytic formulas for the amplitudes are hard to come by except in special limits where things simplify, such as multi-Regge kinematics. By applying symbology we obtain a formula for the leading behavior of the imaginary part (the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics for any number of gluons. Our result predicts a simple recursive structure which agrees with a direct Balitsky-Fadin-Kuraev-Lipatov computation carried out in a parallel publication.
    Physical review D: Particles and fields 04/2012; 85(8).
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    Niklas Beisert, Cristian Vergu
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    ABSTRACT: We discuss various formulations of null polygons in full, non-chiral 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.
    Physical review D: Particles and fields 03/2012; 86(2).
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    ABSTRACT: We compute the one-loop expectation value of light-like polygonal Wilson loops in super-Yang–Mills theory in full superspace. When projecting to chiral superspace, we recover the known results for the tree-level next-to-maximally-helicity-violating scattering amplitude. The one-loop maximally-helicity-violating 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.
    Journal of Physics A Mathematical and Theoretical 01/2012; 45(26). · 1.77 Impact Factor
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    ABSTRACT: We present an integral representation for the parity-even part of the two-loop six-point planar next-to-maximally helicity-violating 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 two-loop order. We also discuss the all-loop structure of the six-point next-to-maximally helicity-violating amplitude and give a parametrization whose dual conformal invariant building blocks have a simple physical interpretation.
    Physical review D: Particles and fields 03/2011; 83(6).
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    ABSTRACT: We present a compact analytic formula for the two-loop six-particle maximally helicity violating remainder function (equivalently, the two-loop lightlike hexagon Wilson loop) in N=4 supersymmetric Yang-Mills 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.
    Physical Review Letters 10/2010; 105(15):151605. · 7.94 Impact Factor
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    ABSTRACT: We revisit the computation of the 2-loop 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 strong-coupling expansion of the generalized scaling function. The computation, using the AdS light-cone 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 2-loop computation we perform involves all the structures in the AdS light-cone gauge superstring action of hep-th/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.
    Journal of High Energy Physics 01/2010; 2010(6):1-51. · 5.62 Impact Factor
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    ABSTRACT: We consider the AdS 5 × S 5 superstring in the light-cone 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 light-cone gauge action by computing the 1-loop and 2-loop 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 non-trivial background. KeywordsField Theories in Lower Dimensions-AdS-CFT Correspondence
    Journal of High Energy Physics 12/2009; 2010(3):1-18. · 5.62 Impact Factor
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    ABSTRACT: AdS4/CFT3 duality relating IIA string theory on AdS4 × 3 to = 6 superconformal Chern-Simons theory provides an arena for studying aspects of integrability in a new potentially exactly solvable system. In this paper we explore the tree-level worldsheet scattering for strings on AdS4 × 3. We compute all bosonic four-, five- and six-point amplitudes in the gauge-fixed action and demonstrate the absence of particle production.
    Journal of High Energy Physics 09/2009; 2009(09):049. · 5.62 Impact Factor
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    C. Vergu
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    ABSTRACT: We compute the even part of the two-loop seven-point planar MHV amplitude in N=4 supersymmetric Yang-Mills 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 all-n 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+1-point MHV amplitude in terms of the integral coefficients of the n-point MHV amplitude.
    Physical review D: Particles and fields 06/2009; 79(12).
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    ABSTRACT: We give a representation of the parity-even part of the planar two-loop six-gluon maximally helicity violating (MHV) amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the Anastasiou-Bern-Dixon-Kosower/Bern-Dixon-Smirnov all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky, and Sokatchev in arXiv:0803.1466. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides nontrivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond.
    Phys. Rev. D. 08/2008; 78(4).
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    ABSTRACT: We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N = 4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal symmetry fixes their form at six points and beyond.
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    ABSTRACT: We present an integral representation for the parity-even part of the two-loop six-point 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 two-loop order. We also discuss the all-loop structure of the six-point NMHV amplitude and give a parametrization whose dual conformal invariant building blocks have a simple physical interpretation.

Publication Stats

299 Citations
32.18 Total Impact Points

Institutions

  • 2012
    • Hochschule für Technik Zürich
      Zürich, Zurich, Switzerland
  • 2009–2011
    • Brown University
      • • Department of Physics
      • • Department of Mathematics
      Providence, RI, United States