Generalized quark-antiquark potentials from a q-deformed AdS[5] × S[5] background

Abstract

We study minimal surfaces with a single cusp in a q-deformed AdS[5] × 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 [J. High Energy Phys. 1106, 131 (2011) [arXiv:1105.5144 [hep-th]]] 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. Finallywe study the near straight-line limit of the potential.