Geometric Properties of QCD String From Willmore Functional

TL;DR

This paper explores the geometric properties of QCD strings by analyzing the extremum of a Willmore-like functional for Riemannian surfaces, revealing insights into the string's stiffness and its relation to geometric parameters.

Contribution

It introduces a geometric framework connecting QCD string parameters with the extremal properties of Riemannian surfaces using Willmore functional analysis.

Findings

World sheet exhibits negative stiffness based on geometric analysis.

Relation established between QCD string action parameters and surface geometry.

Various cases of surface immersion are examined for their geometric implications.

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.