Notes on the scattering amplitude — Wilson loop duality
By S. Caron-Huot. 2010
258 citations recorded by the source corpus.
We consider the duality between the four-dimensional S-matrix of planar maximally supersymmetric Yang-Mills theory and the expectation value of polygonal shaped Wilson loops in the same theory. We extend the duality to amplitudes with arbitrary helicity states by introducing a suitable supersymmetric extension of the Wilson loop. We show that this object is determined by a host of recursion relations, which are valid at tree level and at loop level for a certain “loop integrand” defined within the Lagrangian insertion procedure. These recursion relations reproduce the BCFW ones obeyed by tree-level scattering amplitudes, as well as their extension to loop integrands which appeared recently in the literature, establishing the duality to all orders in perturbation theory. Finally, we propose that a certain set of finite correlation functions can be used to compute all first derivatives of the logarithm of MHV amplitudes.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/573e35593fdb2e79ffb1c298ebceaab2b53c1153
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In Nuclear and High Energy Physics
Citations in the corpus
- Scattering amplitudes and Wilson loops in twistor space (2011, background): “We will frequently abbreviate δ̄0|4(Z1, Z2, Z3, Z4, Z5) by [1, 2, 3, 4, 5].”
- A symbol of uniqueness: the cluster bootstrap for the 3-loop MHV heptagon (2014, background): “Finally, the extension of dual conformal symmetry to dual superconformal symmetry [54], is expressed via the super-Wilson-loop correspondence [55, 56, 57] in terms of recursive differential equations [58, 59] which imply certain universal constraints on the total derivative of the remainder function”
- Bootstrapping an NMHV amplitude through three loops (2014, background): “In general, NMHV scattering amplitudes are dual to Wilson loops dressed with insertions of states that depend on the particular NMHV component being investigated [82, 83].”
- Local integrals for planar scattering amplitudes (2010, background): “This proposal has been checked to satisfy the all-loop recursion relation at the level of the integrand [5], providing a proof of the duality between scattering amplitudes and Wilson-loops [7].”
- Uniqueness of two-loop master contours (2012, unknown): “[74], the super Wilson loop was expressed in the form”
- Space-time S-matrix and flux tube S-matrix II. Extracting and matching data (2013, methodology): “Taking this step enables us to encompass several components of the super Wilson loop [28,29] within the OPE framework [30], besides the usual bosonic loop.”
- Space-time S-matrix and flux-tube S-matrix III. The two-particle contributions (2014, background): “The idea is to engineer the insertions of the fermions on the four edges of a square by deforming a suitably chosen components of a super amplitudes [76, 77], as we now explain.”
- Superconformal symmetry and two-loop amplitudes in planar N = 4 super Yang-Mills (2011, methodology): “The gauge taken in [30] corresponds to step-functions f(t) = θ( − t) and g(t) = θ(t − 1 + ) with very small.”
- When does the gluon reggeize? (2013, background): “[120–123], which naturally led to its proof to all-order in perturbation theory (the amplitude and Wilson loops being both expressed as integrals over the same, recursively constructed, integrands).”
- The four-loop six-gluon NMHV ratio function (2015, background): “The duality between amplitudes and Wilson loops relates NMHV amplitudes to Wilson loops with states inserted on the boundary, with different choices of states corresponding to different NMHV components [98, 99].”