Dual CFT on Nariai limit for Kerr–Sen–dS black holes

Abstract

In this work, we study the Kerr–Sen–de Sitter black hole (BH) in the Nariai limit where the event and cosmological horizon coincide. We show that the near-horizon Kerr–Sen–de Sitter black hole in Nariai limit is a fiber over AdS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} with an appropriate coordinate transformation, instead of fiber over dS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}. Hence, we can compute the associated central charge and CFT temperature by using the Kerr/CFT method. It is remarkably exhibited that through Cardy’s growth of states, the Bekenstein–Hawking entropy on cosmological horizon is reproduced. Moreover, we show that the radial equation of the quantum scalar field in J- and Q-pictures on this charged rotating background in Nariai limit can be portrayed in quadratic Casimir operator form with SL(2,R)×SL(2,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SL(2,R)\ imes SL(2,R)$$\\end{document} isometry. We also compute the corresponding thermodynamic quantities from CFT to find the absorption cross-section and real-time correlator in J-picture. In Q-picture, we do not find a well-defined CFT description. We then extend the study of quantum scalar field in Nariai limit for Kerr–Newman–dS black hole solution and show that the hidden conformal symmetry on this black hole’s background in J- and Q-pictures is well-defined.