Kameyama, Takashi; Yoshida, Kentaroh Generalized quark-antiquark potentials from a \(q\)-deformed \(\mathrm{AdS}_5 \times \mathrm{S}^5\) background. (English) Zbl 1361.81095 PTEP, Prog. Theor. Exper. Phys. 2016, No. 6, Article ID 063B01, 25 p. (2016). Summary: We study minimal surfaces with a single cusp in a \(q\)-deformed \(\mathrm{AdS}_5 \times \mathrm{S}^5\) background. The cusp is composed of two half-lines with an arbitrary angle and is realized on a surface specified in the deformed \(\mathrm{AdS}_5\). The classical string solutions attached to this cusp are regarded as a generalization of configurations studied by N. Drukker and V. Forini [J. High Energy Phys. 2011, No. 6, Paper No. 131, 41 p. (2011; Zbl 1298.81379)] 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. Cited in 4 Documents MSC: 81T13 Yang-Mills and other gauge theories in quantum field theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T20 Quantum field theory on curved space or space-time backgrounds 81R60 Noncommutative geometry in quantum theory 81T75 Noncommutative geometry methods in quantum field theory Citations:Zbl 1298.81379 PDFBibTeX XMLCite \textit{T. Kameyama} and \textit{K. Yoshida}, PTEP, Prog. Theor. Exper. Phys. 2016, No. 6, Article ID 063B01, 25 p. (2016; Zbl 1361.81095) Full Text: DOI arXiv