Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface

TL;DR

This paper explores how conformal SO(2,4) transformations generate new Wilson loop surface configurations in AdS_5, demonstrating their solutions to string equations and calculating their classical actions in IR regularization.

Contribution

It introduces a method to generate diverse Wilson loop surfaces via conformal transformations and evaluates their classical string actions, expanding understanding of Wilson loops in AdS/CFT.

Findings

Generated various two-cusp and four-cusp Wilson loop surfaces from a basic one-cusp surface.

Demonstrated these surfaces solve the string equations of motion.

Calculated classical Euclidean Nambu-Goto actions for these configurations.

Abstract

By applying the conformal SO(2,4) transformations to the elementary one-cusp Wilson loop surface we construct various two-cusp and four-cusp Wilson loop surface configurations in AdS_5 and demonstrate that they solve the string equations of the Nambu-Goto string action. The conformal boosts of the basic four-cusp Wilson loop surface with a square-form projection generate various four-cusp Wilson loop surfaces with projections of the rescaled square, the rhombus and the trapezium, on which surfaces the classical Euclidean Nambu-Goto string actions in the IR dimensional regularization are evaluated.