Generalized quark-antiquark potentials from a $q$-deformed AdS$_5 \times $S$^5$ background

TL;DR

This paper derives a generalized quark-antiquark potential from a $q$-deformed AdS$_5 imes$S$^5$ background, revealing a linear potential at short distances and connecting to noncommutative gauge theories.

Contribution

It introduces a new classical string solution in a $q$-deformed background and derives the corresponding quark-antiquark potential, extending previous undeformed analyses.

Findings

Potential becomes linear at short distances with finite deformation.

Reproduces linear potential behavior of noncommutative gauge theories.

Provides a generalized framework for quark-antiquark interactions in deformed backgrounds.

Abstract

We study minimal surfaces with a single cusp in a $q$-deformed AdS$_5\times$S$^5$ background. The cusp is composed of two half-lines with an arbitrary angle and is realized on a surface specified in the deformed AdS$_5$. The classical string solutions attached to this cusp are regarded as a generalization of configurations studied by Drukker and Forini in the undeformed case. By taking an antiparallel-lines limit, a quark-antiquark potential for the $q$-deformed case is derived with a certain subtraction scheme. The resulting potential becomes linear at short distances with a finite deformation parameter. In particular, the linear behavior for the gravity dual of noncommutative gauge theories can be reproduced as a special scaling limit. Finally we study the near straight-line limit of the potential.