Wilson loops in N=4 SYM theory: rotation in S5

TL;DR

This paper investigates Wilson loops in N=4 SYM theory with scalar field rotations in S5, analyzing their dual string solutions and potential dependence at weak and strong coupling, highlighting differences between Minkowskian and Euclidean frameworks.

Contribution

It provides a detailed analysis of rotating Wilson loops in S5, revealing the absence of direct Minkowskian duals and deriving potential dependencies at various coupling regimes.

Findings

No direct open-string duals for Minkowskian Wilson loops in the rotating case.

The quark-antiquark potential depends on the rotation parameter.

Potential behavior is characterized at both weak and strong coupling.

Abstract

We study Wilson loops in N=4 SYM theory which are non-constant in the scalar (S5) directions and open string solutions associated with them in the context of AdS/CFT correspondence. An interplay between Minkowskian and Euclidean pictures turns out to be non-trivial for time-dependent Wilson loops. We find that in the S5-rotating case there appears to be no direct open-string duals for the Minkowskian Wilson loops, and their expectation values should be obtained by analytic continuation from the Euclidean-space results. In the Euclidean case, we determine the dependence of the ``quark - anti-quark'' potential on the rotation parameter, both at weak coupling (i.e. in the 1-loop perturbative SYM theory) and at strong coupling (i.e. in the classical string theory in AdS5 x S5).