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We show that the near-brane back-reaction of M2 branes ending on M5 branes has a rich "spike structure" that is determined by partitioning the numbers of M2 branes that are terminating on groups of M5 branes. The near-brane limit of the metric describing these branes has an AdS$_3$ factor, implying the existence of a dual CFT. Each partition of the M2 and M5 charges among spikes gives rise to a different "mohawk" revealing a new layer of brane fractionation. We conjecture that all these mohawks are dual to ground states of near-brane-intersection CFT's. We show that the supergravity solutions describing these mohawks are part of the large families of AdS$_3$ $\times S^3 \times S^3$ solutions described in [arXiv:1312.5477]. We identify precisely which of these families are relevant to brane intersections and show that the AdS$_3$ invariance emerges from the self-similarity of the spikes., Comment: 25 pages, 6 figures

We derive a compact formula for the one-loop, bosonic string partition function of Euclideanized $J_3 \bar J_3$ 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 $T \bar T$ 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 $J \bar J$ deformation of a sigma model with $U(1)_L \times U(1)_R$ 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., Comment: 53 pages

Aspects of superstring theory on deformed BTZ black holes, formed near $k$~NS5 branes by $p$~fundamental strings, and single-trace $T\bar T$ 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 $T\bar T$ deformed $CFT_2$ with $c=6k$. 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~$6k$, 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.

We derive various properties of symmetric product orbifolds of $T\bar{T}$ and $J\bar{T}$ - deformed CFTs from a field-theoretical perspective. First, we generalise the known formula for the torus partition function of a symmetric orbifold theory in terms of the one of the seed to non-conformal two-dimensional QFTs; specialising this to seed $T\bar{T}$ and $J\bar{T}$ - deformed CFTs reproduces previous results in the literature. Second, we show that the single-trace $T\bar{T}$ and $J\bar{T}$ deformations preserve the Virasoro and Kac-Moody symmetries of the undeformed symmetric product orbifold CFT, including their fractional counterparts, as well as the KdV charges. Finally, we discuss correlation functions in these theories. By extending a previously-proposed basis of operators for $J\bar{T}$ - deformed CFTs to the single-trace case, we explicitly compute the correlation functions of both untwisted and twisted-sector operators and compare them to an appropriate set of holographic correlators. Our derivations are based mainly on Hilbert space techniques and completely avoid the use of conformal invariance, which is not present in these models., Comment: 50 pp, 5 figures

We construct a two-parameter four-dimensional non-BPS NS-NS smooth microstate solution that asymptotes to flat spacetime with a linear dilaton in type II superstring theory. From the microscopic point of view, the background is made out of a certain number of decoupled (i.e. $g_s\to 0$) NS5 branes wrapping $T^3\times S^1\times S^1$ with fundamental strings wrapping non-contractable cycles of $S^1\times S^1$ with integer momentum modes along them. We show that perturbative worldsheet theory in this background is given by a null-gauged WZW model. We also show that the consistency of the worldsheet theory imposes non-trivial constraints on the supergravity background., Comment: 32 pages

We extend the study of 2006.13249, 2303.12422 to black strings with general momentum, and discuss their interpretation in single-trace $T\bar T$ deformed $CFT_2$., Comment: 16 pages

We explore the holographic duality between string theory in backgrounds that interpolate between asymptotically linear dilaton spacetime in the UV and $AdS_3$ in the IR, and single-trace $T\bar T$ deformed CFT. In particular, we explain how the deformation of states in the boundary theory is reflected in the bulk geometry, and show that the coupling above which the deformed energy of the $SL(2,\mathbb{R})$ invariant ground state of the IR CFT becomes complex is a maximal coupling., Comment: 17 pages

We compute the leading correction to entanglement entropy in $T\bar{T}$ deformed massive QFTs. We show that both for massive scalar and Dirac fermion, the leading order correction to the entanglement entropy of half-space comes from the boundary of the entangling surface. For the case of massive scalar, the boundary term is finite while for massive fermion, it diverges logarithmically giving rise to an additional log-square divergence in the entanglement entropy., Comment: 15 pages

We build a novel time-like coset sigma-model describing type-II superstring theory in a charged rotating black-brane background that interpolates between a locally $AdS_3$ in the IR and a linear-dilaton geometry in the UV. This allows one to perform a systematic study of holography in non-AdS backgrounds which are smoothly connected to $AdS_3$. We construct massless closed string states vertex operators in the NS-NS sector, calculate the corresponding two-point correlation functions, and discuss holographic interpretation of our results from 4+1 dimensional boundary field theory point of view. Compactifying the theory on $\mathbb{T}^4$, we show that the spectrum of a single long string with unit winding agrees with the spectrum of a CFT$_2$ deformed by $T\bar{T}$. We also calculate correlation functions of operators of the dual 1+1 dimensional non-conformal boundary field theory using world-sheet techniques., Comment: 86 pages

We show that the $T \bar T$ deformation of conformal field theories whose entropy grows as $S(E) \sim E^\gamma$ for $\gamma > 1/2$ exhibits negative specific heat in its microcanonical thermodynamic function $S({\cal E})$. We analyze the large $N$ symmetric product CFT as a concrete example of a CFT with this property and compute the thermodynamic functions such as $S({\cal E})$ and ${\cal E}(T)$. The negative specific heat in the microcanonical data is interpreted as signaling the first order phase transition when the system is coupled to a heat bath.

We construct long-range fermionic models with the Gross-Neveu and Gross-Neveu-Yukawa interaction, and argue that their critical regimes are equivalent. To this end, we calculate various CFT data in $\epsilon$- and $1/N$- expansion, and demonstrate their agreement in the overlapping regimes of validity.

We consider the weighted average of a two dimensional CFT, whose target space is $T^2$, over its Narain moduli space. We take as the weighing function the integral kernel which gives rise to $T \bar T$ deformation when applied to the world sheet moduli data of the partition function viewed as vacuum amplitude when the world sheet is a torus. We compute the smeared partition function where this kernel is applied to the target space moduli. Smearing the partition function over the parameter space of a field theory generally leads to the breakdown in the ability to write the partition function as a sum over Boltzmann factor with unit coefficients. The weight function inspired by the $T \bar T$ deformation appears to be an exception to this general expectation. We show that this smearing leads to a marginal deformation corresponding to the overall rescaling of the target space $T^2$., Comment: 15 pages

We study interacting critical UV regime of the long-range $O(N)$ vector model with quartic coupling. Analyzing CFT data within the scope of $\epsilon$- and $1/N$-expansion, we collect evidence for the equivalence of this model and the critical IR limit of the cubic model coupled to a generalized free field $O(N)$ vector multiplet.

In this work, we continue our study of string theory in the background that interpolates between $AdS_3$ in the IR to flat spacetime with a linear dilaton in the UV. The boundary dual theory interpolates between a CFT$_2$ in the IR to a certain two-dimensional Little String Theory (LST) in the UV. In particular, we study \emph{computational complexity} of such a theory through the lens of holography and investigate the signature of non-locality in the short distance behavior of complexity. When the cutoff UV scale is much smaller than the non-locality (Hagedorn) scale, we find exotic quadratic and logarithmic divergences (for both volume and action complexity) which are not expected in a local quantum field theory. We also generalize our computation to include the effects of finite temperature. Up to second order in finite temperature correction, we do not any find newer exotic UV-divergences compared to the zero temperature case., Comment: Appendix A and few references added. 28 pages+1 appendix

In this paper we prove the equivalence among (i) the weakly coupled worldsheet string theory described by the coset sigma model $\frac{SL(2,\mathbb{R})_k\times U(1)}{U(1)}\times S^3 \times T^4$ with $SL(2,\mathbb{R})$ WZW level $k\geq 2$, (ii) the full near horizon theory of the NS5 branes with $k$ NS5 branes wrapping $T^4\times S^1$, $p\gg1$ F1 strings wrapping $S^1$ and $n$ units of momentum along the $S^1$ and (iii) the single trace $T\bar{T}$ deformation of string theory in $AdS_3\times S^3\times T^4$. As a check we compute the spectrum of the spacetime theory by performing BRST quantization of the coset description of the worldsheet theory and show that it matches exactly with the one derived in the case of single trace $T\bar{T}$ deformed string theory in $AdS_3$. Secondly, we compute the two-point correlation function of local operators of the spacetime theory using the worldsheet coset approach and reproduce the same two-point function from the supergravity approach., Comment: 36 pages, 2 figures

We derive the geodesic equation for determining the Ryu-Takayanagi surface in $AdS_3$ deformed by single trace $\mu T \bar T + \varepsilon_+ J \bar T + \varepsilon_- T \bar J$ deformation for generic values of $(\mu, \varepsilon_+, \varepsilon_-)$ for which the background is free of singularities. For generic values of $\varepsilon_\pm$, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta $c$-function. We comment on various features of these observables in the $(\mu, \varepsilon_+, \varepsilon_-)$ parameter space. We discuss the matching at leading order in small $(\mu, \varepsilon_+, \varepsilon_-)$ expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable., Comment: 29 pages, 7 figures

We generalize our recent analysis [2006.13249] of probe string dynamics to the case of general single-trace $T\bar T$, $J\bar T$ and $T\bar J$ deformations. We show that in regions in coupling space where the bulk geometry is smooth, the classical trajectories of such strings are smooth and approach the linear dilaton boundary at either the far past or the far future. These trajectories give rise to quantum scattering states with arbitrarily high energies. When the bulk geometry has closed timelike curves (CTC's), the trajectories are singular for energies above a critical value $E_c$. This singularity occurs in the region with CTC's, and the value of $E_c$ agrees with that read off from the dual boundary theory for all values of the couplings and charges., Comment: 14 pages

In this paper, we continue the study of $T\bar{T}$ deformation in $d=1$ quantum mechanical systems and propose possible analogues of $J\bar{T}$ deformation and deformation by a general linear combination of $T\bar{T}$ and $J\bar{T}$ in quantum mechanics. We construct flow equations for the partition functions of the deformed theory, the solutions to which yields the deformed partition functions as integral of the undeformed partition function weighted by some kernels. The kernel formula turns out to be very useful in studying the deformed two-point functions and analyzing the thermodynamics of the deformed theory. Finally, we show that a non-perturbative UV completion of the deformed theory is given by minimally coupling the undeformed theory to worldline gravity and $U(1)$ gauge theory., Comment: 21 pages + appendices, 1 figure. Few references added in v2

We revisit the idea that the quantum dynamics of open strings ending on $N$ D3-branes in the large $N$ limit can be described at large `t Hooft coupling by classical closed string theory in the background created by the D3-branes in asymptotically flat spacetime. We study the resulting thermodynamics and compute the Hagedorn temperature and other properties of the D3-brane worldvolume theory in this regime. We also consider the theory in which the D3-branes are replaced by negative branes and show that its thermodynamics is well behaved. We comment on the idea that this theory can be thought of as an irrelevant deformation of $\mathcal{N}=4$ SYM, and on its relation to $T\bar T$ deformed $CFT_2$., Comment: 17 pages and 7 figures

String theory on $AdS_3$ has a solvable single-trace irrelevant deformation that is closely related to $T\bar T$. For one sign of the coupling, it leads to an asymptotically linear dilaton spacetime, and a corresponding Hagedorn spectrum. For the other, the resulting spacetime has a curvature singularity at a finite radial location, and an upper bound on the energies of states. Beyond the singularity, the signature of spacetime is flipped and there is an asymptotically linear dilaton boundary at infinity. We study the properties of black holes and fundamental strings in this spacetime, and find a sensible picture. The singularity does not give rise to a hard ultraviolet wall for excitations -- one must include the region beyond it to understand the theory. The size of black holes diverges as their energy approaches the upper bound, as does the location of the singularity. Fundamental strings pass smoothly through the singularity, but if their energy is above the upper bound, their trajectories are singular. From the point of view of the boundary at infinity, this background can be thought of as a vacuum of Little String Theory which contains a large number of negative strings., Comment: 36 pages, 1 figure

We compute the Hagedorn temperature of $\mu T \bar T + \varepsilon_+ J \bar T + \varepsilon_-T \bar J$ deformed CFT using the universal kernel formula for the thermal partition function. We find a closed analytic expression for the free energy and the Hagedorn temperature as a function of $\mu$, $\varepsilon_+$, and $\varepsilon_-$ for the case of a compact scalar boson by taking the large volume limit. We also compute the Hagedorn temperature for the single trace deformed $AdS_3 \times S^1 \times T^3 \times S^3$ using holographic methods. We identify black hole configurations whose thermodynamics matches the functional dependence on $(\mu, \varepsilon_+, \varepsilon_-)$ of the double trace deformed compact scalars., Comment: 18 pages

We explicitly construct every kinematically allowed three particle graviton-graviton-$P$ and photon-photon-$P$ S-matrix in every dimension and for every choice of the little group representation of the massive particle $P$. We also explicitly construct the spacetime Lagrangian that generates each of these couplings. In the case of gravitons we demonstrate that this Lagrangian always involves (derivatives of) two factors of the Riemann tensor, and so is always of fourth or higher order in derivatives. This result verifies one of the assumptions made in the recent preprint \cite{Chowdhury:2019kaq} while attempting to establish the rigidity of the Einstein tree level S-matrix within the space of local classical theories coupled to a collection of particles of bounded spin., Comment: added references

We calculate the spectrum of a two dimensional CFT on a cylinder, perturbed by a general linear combination of $T\bar{T}$, $J\bar{T}$ and $T\bar{J}$, by utilizing the relation of this problem to certain solvable single trace current-current deformations of the worldsheet theory of strings on $AdS_3$. We show that this spectrum is well behaved (i.e. the energies are real) if and only if the dual bulk geometry is well behaved (i.e. the signature of the bulk spacetime is $(1,2)$ and there are no closed timelike curves). We also comment on the relations of string theory on $AdS_3$ and its deformations to symmetric product CFT's, matrix string theory, and a black hole description of highly excited fundamental strings., Comment: 44 pages

We consider deformation of a generic $d$ dimensional ($d\geq 2$) large-$N$ CFT on a sphere by a spin-0 operator which is bilinear in the components of the stress tensor. Such a deformation has been proposed to be holographically dual to an $AdS_{d+1}$ bulk with a hard radial cut-off. We compute the exact partition function and find the entanglement entropy from the field theory side in various dimensions and compare with the corresponding holographic results. We also compute renormalized entanglement entropy both in field theory and holography and find complete agreement between them., Comment: Comments and clarifications added, references updated, version to appear in Nucl. Phys. B

In this paper we study string theory in the background $\mathcal{M}_3$ that interpolates between $AdS_3$ in the IR and linear dilaton spacetime $\mathbb{R}^{1,1}\times\mathbb{R}_\phi$ in the UV. Via holographic duality this background corresponds to $\rm{CFT}_2$ deformed by a dimension $(2,2)$ operator. Here we discuss the holographic Wilson loop in such a model and shed more light in support of the non-local structure of the theory (Little String Theory (LST)) in the UV. We also discuss quantum and thermal phase transitions of the boundary theory., Comment: 19 pages, 7 figures

We study two dimensional conformal field theory with a left-moving conserved current $J$, perturbed by an irrelevant, Lorentz symmetry breaking operator with the quantum numbers of $J\bar{T}$, using a combination of field and string theoretic techniques. We show that the spectrum of the theory has some interesting features, which may shed light on systems of interest for holography and black hole physics., Comment: 38 pages, references added

We continue our study of string theory in a background that interpolates between $AdS_3$ in the infrared and a linear dilaton spacetime $R^{1,1}\times R_\phi$ in the UV. This background corresponds via holography to a $CFT_2$ deformed by an operator of dimension $(2,2)$. We discuss the structure of spatial entanglement in this model, and compare it to the closely related $T\bar T$ deformed $CFT_2$., Comment: 22 pages, 7 figures

We investigate the behavior of shear viscosity in the presence of small anisotropy and a finite chemical potential. First, we construct an anisotropic Reissner Nordstr{\"o}m blackbrane in 5 dimensions in a simple Einstein-Maxwell theory with a small linear dilaton. This solution is characterized by three mass scales : anisotropy $\rho$, temperature T and chemical potential $\mu$. We find this solution upto second order in the dilaton anisotropy parameter $\rho$. This blackbrane solution corresponds to an anisotropic phase where the anisotropy is small compared to the temperature and chemical potential. We find that in this anisotropic phase, some components of the anisotropic shear viscosity tensor, which are spin one with respect to the residual symmetry after breaking rotational invariance, violates the KSS bound (${\eta \over s}\ge {1 \over 4 \pi} $) proposed by Kovtun, Son and Starinets. We identify the regions of the parameter space where these violations are significant. We carry out a similar analysis in 4 dimensions and find similar violation of the KSS bound for the spin one components to demonstrate the generality of the result. Our results are particularly relevant in the context of strongly coupled systems found in nature. We also provide an intuitive understanding of the results using dimensional reduction and a Boltzmann calculation in a weakly coupled version of a similar system. The Boltzmann analysis performed in a system of weakly interacting particles in a linear potential also shows that components of the viscosity tensor may be reduced. It is intriguing that the Boltzmann analysis also predicts the corrections to be negative and that too in a manner similar to the anisotropic strongly coupled theories with smooth gravity duals., Comment: References added, minor changes, appendix added

MacKey constructed a set of induced representation character formulas to calculate the sum of different powers of the eigenvalues of a matrix with finite group symmetry. We show that these results of MacKey can be used to derive the stability condition, m > Cn3, of Maxwell using his symmetric model for a ring of Saturn, as a collection of n identical unit mass particles revolving round Saturn, which has mass m, in a circular orbit.