Aspects of superstring theory on black-strings backgrounds, corresponding to deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace TT(sic) +JT(sic) +TJ(sic) 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 TT(sic) +JT(sic) +TJ(sic) deformed CFT2 with c = 6k. 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.

Aspects of superstring theory on black-strings backgrounds, corresponding to deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace TT+JT+TJ 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 TT+JT+TJ deformed CFT2 with c = 6k. 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 Zw twisted sector of a p-fold symmetric product of the latter.

Abstract Aspects of superstring theory on black-strings backgrounds, corresponding to deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace T T ¯ + J T ¯ + T J ¯ $$ T\overline{T}+J\overline{T}+T\overline{J} $$ 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 T ¯ + J T ¯ + T J ¯ $$ T\overline{T}+J\overline{T}+T\overline{J} $$ deformed CFT 2 with c = 6k. 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.

Superstring theory on black-strings backgrounds, corresponding to deformed, rotating BTZ black holes, formed near k NS5 branes 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, 1/p fraction of the black-string energy, is the same as that in TT¯ deformed CFT2 with c=6k, if the B-field vanishes at the origin. This supports the claim that the black string can be thought of as a state in a symmetric product of p CFT2's with central charge c=6k, where the black-string energy is split equally among all p factors. In [1], it was not verified that this property persists in other cases. Here, we generalize the investigation of [1] to the superstring on deformed, rotating BTZ black holes, for both the positive and negative cases. We find the particular value of the B-field at the origin, for which the total energy of a probe long string, consisting of its excitation energy plus its contribution to the 1/p fraction of the black-string energy, is the same as that in TT¯ deformed CFT2 with c=6k. Interestingly, the B-field required for this harmony with single-trace TT¯ holography, does not vanish at the origin in the rotating cases.

In [1], we argued that the (0, 2) heterotic string gives rise in spacetime to left and right-moving symmetric product CFT’s. In this paper we confirm this claim by showing that it computes correlation functions in these CFT’s.

Abstract 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 T ¯ $$ T\overline{T} $$ deformation of the free theory.

Aspects of superstring theory on black-strings backgrounds, corresponding to deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace TT̅+JT̅+TJ̅ 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 TT̅+JT̅+TJ̅ deformed CFT_2 with c=6k. 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.

We revisit the fermionic string theory on AdS_3×𝒩 with k = 1, and its single-trace TT deformation, with a focus on the (2, 2) superstring on (deformed) AdS_3×𝕋^3 . In a certain limit, it is dual to the symmetric product of the ( TT -deformed) SCFT2 on ℝ×𝕋^3 . We present the winding-one delta-function normalizable worldsheet operators which, in the k = 1 decoupling limit, correspond to those of ℝ×𝕋^3 in spacetime. We then demonstrate how their properties in string theory reproduce those of ℝ×𝕋^3 , or more generally, of a ( TT -deformed) ℝ×𝒩 seed of the boundary theory.

Abstract In [1], it was pointed out that superstring theory on AdS 3 with (NS, NS) B-field background and R AdS/l s = k $$ \sqrt{k} $$ < 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.

Abstract 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) SCFT2 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 AdS3 x N with k = 1, and its single-trace TT deformation, with a focus on the (2, 2) superstring on (deformed) AdS3 x T3. In a certain limit, it is dual to the symmetric product of the (TT-deformed) SCFT2 on R x T3. We present the winding-one delta-function normalizable worldsheet operators which, in the k = 1 decoupling limit, correspond to those of R x T3 in spacetime. We then demonstrate how their properties in string theory reproduce those of R x T3, or more generally, of a (TT-deformed) R x N seed of the boundary theory.

We show that 1 + 1 dimensional vacua of the(0,2)heterotic string have manyproperties in common with more recently studied physical systems. The free theory exhibits asymmetric 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 (forw <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 aT T deformation of the free theory

In [2109.00065], it was pointed out that superstring theory on AdS_3 with (NS,NS) B-field background and R_AdS/l_s=√(k)<1 is dual to a symmetric product CFT deformed by an operator in the ℤ_2 twisted sector. We generalize the analysis of [2109.00065] to k>1, and show that the resulting picture matches that discussed in the bosonic case in [2110.07535]. We argue that in the critical case, k=1 [0503121], the ℤ_2 twisted deformation remains non-trivial. This resolves some confusions in the literature.

In [1], it was pointed out that superstring theory on AdS3 with (NS, NS) B-field background and RAdS/ls = √(k) < 1 is dual to a symmetric product CFT deformed by an operator in the ℤ2 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 ℤ2 twisted deformation remains non-trivial. This resolves some confusions in the literature.

Superstring theory on black-strings backgrounds, corresponding to deformed, rotating BTZ black holes, formed near k NS5 branes 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, 1/P fraction of the black-string energy, is the same as that in T (T) over bar deformed CFT2 with c = 6k, if the B-field vanishes at the origin. This supports the claim that the black string can be thought of as a state in a symmetric product of P CFT2's with central charge c = 6k, where the black-string energy is split equally among all P factors. In [1], it was not verified that this property persists in other cases. Here, we generalize the investigation of [1] to the superstring on deformed, rotating BTZ black holes, for both the positive and negative cases. We find the particular value of the B-field at the origin, for which the total energy of a probe long string, consisting of its excitation energy plus its contribution to the 1/P fraction of the black-string energy, is the same as that in T (T) over bar deformed CFT2 with c = 6k. Interestingly, the B-field required for this harmony with single-trace T (T) over bar holography, does not vanish at the origin in the rotating cases.

We continue our exploration of the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and AdS3 in the IR, and the corresponding boundary theories. In previous papers, [1], [2], we showed that states in the bulk theory that are described by non-trivial asymptotically linear dilaton geometries, such as black holes and deformed global AdS3, can be described in the boundary theory by a single-trace TT¯ deformation of a symmetric product theory. In those papers, we restricted to states with vanishing (angular) momentum; in this paper, we extend the analysis to states with arbitrary momentum, and show that the picture presented in the earlier papers generalizes to this case.

Abstract We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized J 3 J ¯ 3 $$ {J}_3{\overline{J}}_3 $$ 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 T ¯ $$ T\overline{T} $$ 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 J ¯ $$ J\overline{J} $$ 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.

Aspects of superstring theory on deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace TT 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 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.

We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized J(3)(J) over bar (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 (T) over bar 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 (J) over bar deformation of a sigma model with U(1)(L) x 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.

A bstract Aspects of superstring theory on deformed BTZ black holes, formed near k NS5 branes by p fundamental strings, and single-trace $$ T\overline{T} $$ T T ¯ 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 $$ T\overline{T} $$ T T ¯ deformed CFT 2 with c = 6 k . This supports the claim that the black hole can be thought of as a state in a symmetric product of p CFT 2 ’s of central charge 6 k , where the black-hole energy is split equally among all p factors. A comment on superstring theory on deformed global AdS 3 is also presented.