From spacetime to worldsheet: four point correlators

The Schwinger representation gives a systematic procedure for recasting largeN field theory amplitudes as integrals over closed string moduli space. Thisprocedure has recently been applied to a class of free field four pointfunctions by Aharony, Komargodski and Razamat, to study the leading terms inthe putative worldsheet OPE. Here we observe that the dictionary betweenSchwinger parameters and the cross ratio of the four punctured sphere actuallyyields an explicit expression for the full worldsheet four point correlator inmany such cases. This expression has a suggestive form and obeys variousproperties, such as crossing symmetry and mutual locality, expected of acorrelator in a two dimensional CFT. Therefore one may take this to be acandidate four point function in a worldsheet description of closed strings onhighly curved AdS_5 \times S^5. The general framework, that we develop forcomputing the relevant Strebel differentials, also admits a systematicperturbation expansion which would be useful for studying more general fourpoint correlators.Comment: 41 pages, uses JHEP3.cl