Equivalence of twistor prescriptions for super Yang-Mills

TL;DR

This paper demonstrates the equivalence of different twistor space methods for computing super Yang-Mills amplitudes by relating them through integrals over moduli spaces of singular curves, and introduces new intermediate prescriptions.

Contribution

It establishes the equivalence of connected and disconnected twistor prescriptions for super Yang-Mills amplitudes and proposes novel intermediate methods.

Findings

Connected and disconnected prescriptions are equivalent with specific contour choices.

Both methods reduce to the same integral over a moduli space of singular curves.

New intermediate prescriptions are formulated for amplitude calculations.

Abstract

There is evidence that one can compute tree level super Yang-Mills amplitudes using either connected or completely disconnected curves in twistor space. We argue that the two computations are equivalent, if the integration contours are chosen in a specific way, by showing that they can both be reduced to the same integral over a moduli space of singular curves. We also formulate a class of new ``intermediate'' prescriptions to calculate the same amplitudes.