Amit Giveon

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.

A bstract: We revisit the fermionic string theory on $$Ad{S}_{3}\times \mathcal{N}$$ with k = 1, and its single-trace $$T\overline{T }$$ deformation, with a focus on the (2, 2) superstring on (deformed) $$Ad{S}_{3}\times {\mathbb{T}}^{3}$$ . In a certain limit, it is dual to the symmetric product of the ( $$T\overline{T }$$ -deformed) SCFT ₂ on $${\mathbb{R}}\times {\mathbb{T}}^{3}$$ . We present the winding-one delta-function normalizable worldsheet operators which, in the k = 1 decoupling limit, correspond to those of $${\mathbb{R}}\times {\mathbb{T}}^{3}$$ in spacetime. We then demonstrate how their properties in string theory reproduce those of $${\mathbb{R}}\times {\mathbb{T}}^{3}$$ , or more generally, of a ( $$T\overline{T }$$ -deformed) $${\mathbb{R}}\times \mathcal{N}$$ seed of the boundary theory.

We revisit the fermionic string theory on $AdS_3\times \mathcal{N}$ with $k=1$, and its single-trace $T\bar T$ deformation, with a focus on the $(2,2)$ superstring on (deformed) $AdS_3\times \mathbb{T}^3$. In a certain limit, it is dual to the symmetric product of the ($T\bar T$-deformed) SCFT$_2$ on $\mathbb{R}\times \mathbb{T}^3$. We present the winding-one delta-function normalizable worldsheet operators which, in the $k=1$ decoupling limit, correspond to those of $\mathbb{R}\times \mathbb{T}^3$ in spacetime. We then demonstrate how their properties in string theory reproduce those of $\mathbb{R}\times\mathbb{T}^3$, or more generally, of a ($T\bar{T}$-deformed) $\mathbb{R}\times\mathcal{N}$ seed of the boundary theory.

We show that 1 + 1 dimensional vacua of the (0, 2) heterotic string have many properties in common with more recently studied physical systems. The free theory exhibits a symmetric product CFT structure. The single-string Hilbert space splits into sectors labeled by the string winding, w, that contain purely left-moving (for w > 0) and right-moving (for w < 0) excitations. These sectors exhibit infinite-dimensional left and right-moving symmetry algebras, respectively, with central extensions that depend on w. String interactions between left and right-movers appear to lead to a $$ T\overline{T} $$ T T ¯ deformation of the free theory.

In [1], it was pointed out that superstring theory on AdS ₃ with (NS, NS) B-field background and R _AdS/l _s = $$ \sqrt{k} $$ k < 1 is dual to a symmetric product CFT deformed by an operator in the ℤ ₂ twisted sector. We generalize the analysis of [1] to k > 1, and show that the resulting picture matches that discussed in the bosonic case in [2]. We argue that in the critical case, k = 1 [3], the ℤ ₂ twisted deformation remains non-trivial. This resolves some confusions in the literature.

We show that $1+1$ dimensional vacua of the $(0,2)$ heterotic string have many properties in common with more recently studied physical systems. The free theory exhibits a symmetric product CFT structure. The single-string Hilbert space splits into sectors labeled by the string winding, $w$, that contain purely left-moving (for $w>0$) and right-moving (for $w<0$) excitations. These sectors exhibit infinite-dimensional left and right-moving symmetry algebras, respectively, with central extensions that depend on $w$. String interactions between left and right-movers appear to lead to a $T\bar T$ deformation of the free theory.

Superstring theory on black-strings backgrounds, corresponding to deformed, rotating BTZ black holes, formed by $p$ fundamental strings or negative strings, is inspected. For non-rotating black strings, in the positive case, it was shown in [1] that the excitation energy of a probe long string, plus its contribution to the black-string background, is in harmony with single-trace $T\bar T$ holography, if the $B$-field vanishes at the origin. Here, we investigate the superstring on deformed, rotating BTZ black holes, for both the positive and negative cases, and find that for a particular value of the $B$-field, the harmony with single-trace $T\bar T$ holography persists.

We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized $$ {J}_3{\overline{J}}_3 $$ J 3 J ¯ 3 deformed AdS ₃ with periodic Euclidean time as an integral transform of the partition function of the undeformed Euclideanized AdS ₃. Such a deformation is interpretable as an irrelevant “single-trace $$ T\overline{T} $$ T T ¯ deformation” of the boundary. We will do this by first establishing a formal procedure to compute a worldsheet torus zero point function for an exactly marginal $$ J\overline{J} $$ J J ¯ deformation of a sigma model with U(1) _L × U(1) _R global symmetry. We then describe how this procedure is implemented on SL(2, R) sigma model and its Euclidean continuation. Finally, we describe the embedding of the deformed SL(2, R) torus amplitude into critical string theory and interpret the result as the leading perturbative contribution to the thermal partition function of the deformed theory.