Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models

Understand

We propose that, in N=4 Super Yang-Mills theory, correlation functions of certain 1/8 BPS Wilson loops and local operators inserted on a S^2 in space-time may be computed in terms of analogous observables in the "zero-instanton" sector of 2d Yang-Mills theory.

• The Wilson loops are mapped to the standard Wilson loops of the 2d theory, as recently conjectured, while the local operators are mapped to powers of the 2d field strength.
• We give several perturbative checks of the correspondence, and derive from 2d Yang-Mills a two-matrix model for the correlator of a local operator and a Wilson loop of arbitrary shape.
• We show that the strong coupling planar limit of the two-matrix model precisely agrees with a string theory calculation in AdS_5 x S^5.