Probing N=4 SYM With Surface Operators

In this paper we study surface operators in N=4 supersymmetric Yang-Mills theory. We compute surface operator observables, such as the expectation value of surface operators, the correlation function of surface operators with local operators, and the correlation function of surface operators with Wilson and ‘t Hooft loops. The calculations are performed using three different realizations of surface operators, corresponding respectively to the gauge theory path integral definition, the probe brane description in AdS_5xS^5 and the "bubbling’’ supergravity description of surface operators. We find remarkable agreement between the different calculations performed using the three different realizations.