On string theory on deformed BTZ and $$ T\overline{T}+J\overline{T}+T\overline{J} $$

A bstract Aspects of superstring theory on black-strings backgrounds, corresponding to deformed BTZ black holes, formed near k NS 5 branes by p fundamental strings, and single-trace $$ T\overline{T}+J\overline{T}+T\overline{J} $$ T T ¯ + J T ¯ + T J ¯ holography, are presented. It is shown that for a particular asymptotic value of the B -field, the excitation energy of a long string plus its contribution to the energy of the black hole is that in $$ T\overline{T}+J\overline{T}+T\overline{J} $$ T T ¯ + J T ¯ + T J ¯ deformed CFT 2 with c = 6 k . The excitation energy of a winding w > 1 long string plus its contribution to the background, a w/p fraction of the black-hole energy, evolves according to that in a Z w twisted sector of a p -fold symmetric product of the latter.