Ope between the Energy-momentum Tensor and the Wilson Loop in N = 4 Super-yang-mills Theory Typeset Using Ptpt E X.sty <ver.1.0> 2

Conformal field theory (CFT) is important in modern particle physics in various contexts. The most powerful tool in the 2-dimensional CFT is the operator product expansion (OPE). The OPE between the energy-momentum tensor and an operator extracts its conformal weight. We find it interesting to consider the similar issue with respect to the Wilson loop in a conformally invariant Yang-Mills theory. We investigate the OPE between the energy-momentum tensor and the Wilson loop in N = 4 4-dimensional Super-YangMills (SYM) theory with U(N) gauge group by means of the dimensional analysis and the properties of the energy-momentum tensor. We clarify that the Wilson loop in N = 4 SYM theory does not possess an anomalous dimension and that only the deformation of the loop occurs under the conformal transformation. Another interesting issue is the AdS/CFT correspondence 1). The AdS/CFT correspondence enables one to evaluate such physical quantities as the multi-point function 4) and the expectation value of the Wilson loop 2) 3) in strong coupling region. Yet, there have been ambitious attempts to compute the expectation value of the Wilson loop in strong coupling region by means of the quantum field theory 6) 7) for a direct test of AdS/CFT correspondence. Especially, Gross and Drukker 7) pointed out that the expectation value of the circular Wilson loop in N = 4 4-dimensional SYM theory is determined by an anomaly in the conformal transformation that relates the circular loop to the straight line, and computed the expectation value of the circular Wilson loop to all orders in the 1 N2 expansion. However, their analysis is based on the Feynman gauge, and the generalization to the general gauge is nontrivial. We attempt to grasp the conformal anomaly via the OPE between the energy-momentum tensor and the closed Wilson loop, taking advantage of its gauge invariance. This paper is organized as follows. Sec. 2. is devoted to the OPE between