Geometric Properties of QCD String From Willmore Functional

Abstract

The extremum of the Willmore-like functional for $m$-dimensional Riemannian surface immersed in $d$-dimensional Riemannian manifold under normal variations is studied and various cases of interest are examined. This study is used to relate the parameters of QCD string action, including the Polyakov-Kleinert extrinsic curvature action, with the geometric properties of the world sheet. The world sheet has been shown to have {\it{negative stiffness}} on the basis of geometric considerations.