Abstract
Pentagon Operator Product Expansion provides a non-perturbative framework for analysis of scattering amplitudes in planar maximally supersymmetric gauge theory building up on their duality to null polygonal superWilson loop and integrability. In this paper, we construct a systematic expansion for the main ingredients of the formalism, i.e., pentagons, at large 't Hooft coupling as a power series in its inverse value. The calculations are tested against relations provided by the so-called Descent Equation which mixes transitions at different perturbative orders. We use leading order results to have a first glimpse into the structure of scattering amplitude at NMHV level at strong coupling.
Highlights
[1] Operator Product Expansion [2] for superWilson loop WN on a null polygonal contour paved a way for unravelling analytical structure of scattering superamplitude AN of N particles, they are dual to [3, 4, 5, 6, 7, 8], at any value of ’t Hooft coupling in planar maximally supersymmetric Yang-Mills theory
The pentagon transitions at strong coupling are found by substituting the above result (3.56) into the expressions for pentagons derived in Appendix B.1, PG|G(u1|u2) = wGG(u1, u2)PG|G (u1|u2)
In this paper we initiated a systematic study of the strong coupling expansion for pentagon transitions in the OPE approach to the null polygonal superWilson loop
Summary
The formulation of the Pentagon [1] Operator Product Expansion [2] for superWilson loop WN on a null polygonal contour paved a way for unravelling analytical structure of scattering superamplitude AN of N particles, they are dual to [3, 4, 5, 6, 7, 8], at any value of ’t Hooft coupling in planar maximally supersymmetric Yang-Mills theory. Compared to other excitations,—fermions, gluons and bound states thereof,— scalars, known as holes, possess exponentially vanishing masses at strong coupling, potentially producing leading order contribution in the multi-collinear kinematics, i.e., τi → ∞ Their effect in the amplitude is formally suppressed by inverse coupling relative to semiclassical string effects and, for this reason, we will ignore holes in the nonperturbative regime, though they were shown to provide an additive geometry-independent constant contribution to the minimal area due to their intricate infrared dynamics when resummed to all orders [19]. For the gauge fields and bound states, the physical region of ucorresponds to the interval (−1, 1), while for fermions, uresides on the small fermion sheet containing the point of the fermion at rest and varies over two semi-infinite segments u ∈ (−∞, −1) ∪ (1, ∞) It is for these values, the energy E and momentum p of these flux-tube excitations are of order one in g, i.e., E, p ∼ g0. Several appendices contain compendium of integrals needed for calculations involved as well as a list of results which are two cumbersome to be quoted in the main text
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