On string theory on deformed BTZ and TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textrm{T}\overline{\textrm{T}} $$\end{document}

Aspects of superstring theory on deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} holography, are presented. The excitation energy of a singly wound long string plus its contribution to the energy of the black hole, 1/p fraction of the black-hole energy, is the same as that in TT¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ T\overline{T} $$\end{document} deformed CFT2 with c = 6k. This supports the claim that the black hole can be thought of as a state in a symmetric product of p CFT2’s of central charge 6k, where the black-hole energy is split equally among all p factors. A comment on superstring theory on deformed global AdS3 is also presented.