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Nonsinglet pentagons and NHMV amplitudes,” arXiv:1407.2853 [hepth
"... Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the ..."
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Scattering amplitudes in maximally supersymmetric gauge theory receive a dual description in terms of the expectation value of the super Wilson loop stretched on a null polygonal contour. This makes the analysis amenable to nonperturbative techniques. Presently, we elaborate on a refined form of the operator product expansion in terms of pentagon transitions to compute twisttwo contributions to NMHV amplitudes. To start with, we provide a novel derivation of scattering matrices starting from Baxter equations for fluxtube excitations propagating on magnon background. We propose bootstrap equations obeyed by pentagon form factors with nonsinglet quantum numbers with respected to the Rsymmetry group and provide solutions to them to all orders in ’t Hooft coupling. These are then successfully confronted against available perturbative calculations for NMHV amplitudes to threeloop order. ar X iv
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"... We analyze the nearcollinear limit of the null polygonal hexagon super Wilson loop in the planar N = 4 superYangMills theory. We focus on its Grassmann components which are dual to nexttomaximally helicityviolating (NMHV) scattering amplitudes. The kinematics in question is studied within a fra ..."
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We analyze the nearcollinear limit of the null polygonal hexagon super Wilson loop in the planar N = 4 superYangMills theory. We focus on its Grassmann components which are dual to nexttomaximally helicityviolating (NMHV) scattering amplitudes. The kinematics in question is studied within a framework of the operator product expansion that encodes propagation of excitations on the background of the color flux tube stretched between the sides of Wilson loop contour. While their dispersion relation is known to all orders in ’t Hooft coupling from previous studies, we find their form factor couplings to the Wilson loop. This is done making use of a particular tessellation of the loop where pentagon transitions play a fundamental role. Being interested in NMHV amplitudes, the corresponding building blocks carry a nontrivial charge under the SU(4) Rsymmetry group. Restricting the current consideration to twisttwo accuracy, we analyze twoparticle contributions with a fermion as one of the constituents in the pair. We demonstrate that these nonsinglet pentagons obey bootstrap equations that possess consistent solutions for any value of the coupling constant. To confirm the correctness of these predictions, we calculate their contribution to the super Wilson loop demonstrating agreement with recent results to threeloop order. ar X iv
Hexagon Wilson Loop OPE and Harmonic Polylogarithms
"... A recent, integrabilitybased conjecture in the framework of the Wilson loop OPE for N = 4 SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form. We prove that these integrals evaluate to a particular basis of ..."
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A recent, integrabilitybased conjecture in the framework of the Wilson loop OPE for N = 4 SYM theory, predicts the leading OPE contribution for the hexagon MHV remainder function and NMHV ratio function to all loops, in integral form. We prove that these integrals evaluate to a particular basis of harmonic polylogarithms, at any order in the weak coupling expansion. The proof constitutes an algorithm for the direct computation of the integrals, which we employ in order to obtain the full (N)MHV OPE contribution in question up to 6 loops, and certain parts of it up to 12 loops. We attach computerreadable files with our results, as well as an algorithm implementation which may be readily used to generate higherloop corrections. The feasibility of obtaining the explicit kinematical dependence of the first term in the OPE in principle at arbitrary loop order, offers promise for the suitability of this approach as a nonperturbative description of Wilson loops/scattering amplitudes. 1Email address:
Prepared for submission to JHEP DESY 14057 Wilson loop OPE, analytic continuation and multiRegge limit
"... Abstract: We explore a direct connection between the collinear limit and the multiRegge limit for scattering amplitudes in the N = 4 super YangMills theory. Starting with the collinear expansion for the sixgluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term ..."
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Abstract: We explore a direct connection between the collinear limit and the multiRegge limit for scattering amplitudes in the N = 4 super YangMills theory. Starting with the collinear expansion for the sixgluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the socalled Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multiRegge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the “collinearRegge ” limit up to five loops. Our results agree with all the known results up to four loops. At fiveloop, our results up to the nexttonexttoleading logarithmic approximation (NNLLA) also reproduce the known results, and for the N3LLA and the N4LLA give nontrivial predictions. We further present an allloop prediction for the imaginary part of the nexttodoubleleading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multiRegge limit with the help of the OPE. ar X iv
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"... We compute threepoint functions of general operators in the su(11) sector of planar N = 4 SYM in the weak coupling regime, both at treelevel and oneloop. Each operator is represented by a closed spin chain Bethe state characterized by a set of momenta parameterizing the fermionic excitations. At ..."
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We compute threepoint functions of general operators in the su(11) sector of planar N = 4 SYM in the weak coupling regime, both at treelevel and oneloop. Each operator is represented by a closed spin chain Bethe state characterized by a set of momenta parameterizing the fermionic excitations. At oneloop, we calculate both the twoloop Bethe eigenstates and the relevant Feynman diagrams for the threepoint functions within our setup. The final expression for the structure constants is surprisingly simple and hints at a possible form factor based approach yet to be unveiled. ar X iv
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"... Prepared for submission to JHEP Adjoint BFKL at finite coupling: a shortcut from the collinear limit aBenjamin Basso, b,cSimon CaronHuot and cAmit Sever ..."
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Prepared for submission to JHEP Adjoint BFKL at finite coupling: a shortcut from the collinear limit aBenjamin Basso, b,cSimon CaronHuot and cAmit Sever
Threepoint functions and su(11) spin chains
, 2014
"... Abstract: We compute threepoint functions of general operators in the su(11) sector of planar N = 4 SYM in the weak coupling regime, both at treelevel and oneloop. Each operator is represented by a closed spin chain Bethe state characterized by a set of momenta parameterizing the fermionic excit ..."
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Abstract: We compute threepoint functions of general operators in the su(11) sector of planar N = 4 SYM in the weak coupling regime, both at treelevel and oneloop. Each operator is represented by a closed spin chain Bethe state characterized by a set of momenta parameterizing the fermionic excitations. At oneloop, we calculate both the twoloop Bethe eigenstates and the relevant Feynman diagrams for the threepoint functions within our setup. The final expression for the structure constants is surprisingly simple and hints at a possible form factor based approach yet to be unveiled.