Worldsheet Fluctuations and the Heavy Quark Potential in the AdS/CFT Approach

TL;DR

This paper investigates how fluctuations of the string worldsheet in AdS space affect the heavy quark potential in gauge theories, revealing near-flat space eigenvalues and potential implications for string models.

Contribution

It introduces a detailed analysis of worldsheet fluctuations in AdS/CFT, highlighting the emergence of massive modes and their possible connection to effective string theories.

Findings

Eigenvalues of fluctuations are close to flat space values.

Two transverse fields become massive, affecting potential corrections.

Implications for Lüscher term and extrinsic curvature in string models.

Abstract

We consider contributions to the heavy quark potential, in the AdS/CFT approach to SU(N) gauge theory, which arise from first order fluctuations of the associated worldsheet in anti-deSitter space. The gaussian fluctuations occur around a classical worldsheet configuration resembling an infinite square well, with the bottom of the well lying at the AdS horizon. The eigenvalues of the corresponding Laplacian operators can be shown numerically to be very close to those in flat space. We find that two of the transverse world sheet fields become massive, which may have implications for the existence of a L{\"u}scher term in the heavy quark potential. It is also suggested that these massive degrees of freedom may relate to extrinsic curvature in an effective D=4 string theory.