Dynamics of a wavy plane Wilson surface observable from AdS-CFT correspondence

TL;DR

This paper investigates the behavior of a wavy plane Wilson surface observable within the AdS-CFT framework, revealing that a critical dimension D=6 is necessary for certain surface equations to hold in the large N limit.

Contribution

It computes the second variational derivative of the Wilson surface and identifies the critical dimension D=6 for the surface equation to be satisfied.

Findings

Critical dimension for the surface equation is D=6.

Second variational derivative computed for the Wilson surface.

Supports the theoretical understanding of Wilson surfaces in AdS-CFT.

Abstract

Guided by the paper hep-th/0002106 by Polyakov and Rychkov, we compute the second variational derivative of a wavy plane Wilson surface observable, to find that a necessary condition for a proposed surface equation to be satisfied in the large $N$ limit is that we are in the critical dimension D=6.