Associativity and symmetry determine the all-loop 2d chiral algebra OPEs for twistorial self-dual Yang-Mills, with one coefficient, c, left only as an order-by-order solution.
One Loop Multiphoton Helicity Amplitudes
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We use the solutions to the recursion relations for double-off-shell fermion currents to compute helicity amplitudes for $n$-photon scattering and electron-positron annihilation to photons in the massless limit of QED. The form of these solutions is simple enough to allow {\it all}\ of the integrations to be performed explicitly. For $n$-photon scattering, we find that unless $n=4$, the amplitudes for the helicity configurations (+++...+) and (-++...+) vanish to one-loop order.
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Associativity is enough: an all-orders 2d chiral algebra for 4d form factors
Associativity and symmetry determine the all-loop 2d chiral algebra OPEs for twistorial self-dual Yang-Mills, with one coefficient, c, left only as an order-by-order solution.