Twistor coverings and Feynman diagrams

Abstract

Recently, a worldsheet dual to free mathcal{N} = 4 Super Yang-Mills has been proposed in terms of twistor variables for AdS5, in parallel to that for the AdS3 dual to the free symmetric orbifold CFT. In the latter case, holomorphic covering maps play a central role in determining correlators and are associated to Feynman diagrams. After recasting these maps in terms of the worldsheet twistor variables for AdS3, we generalise to AdS5. We propose stringy incidence relations and appropriate reality conditions for the twistor covering maps. For some special kinematic configurations of correlators, we exhibit an explicit construction of the corresponding covering map. We find that the closed string worldsheet corresponding to this map is related to a gauge theory Feynman diagram by the Strebel construction, as for AdS3/CFT2. Rather strikingly, the regularised Strebel area of the worldsheet reproduces the Feynman propagator of the free field theory.