M5-branes and D4-branes wrapped on a direct product of spindle and Riemann surface

Abstract

We construct multi-charged AdS3× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} and AdS2× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} solutions from M5-branes and D4-branes wrapped on a direct product of spindle, ⅀, and Riemann surface, Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document}. Employing uplift formula, we obtain these solutions by uplifting the multi-charged AdS3× ⅀ and AdS2× ⅀ solutions to seven and six dimensions, respectively. We further uplift the solutions to eleven-dimensional and massive type IIA supergravity and calculate the holographic central charge and the Bekenstein-Hawking entropy, respectively. We perform the gravitational block calculations and, for the AdS3× ⅀ ×Σg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\Sigma}_{\\mathfrak{g}} $$\\end{document} solutions, the result precisely matches the holographic central charge from the supergravity solutions.