arXiv subjects
Publications and source records attributed to Soumangsu Chakraborty.
We study interacting critical UV regime of the long-range $O(N)$ vector model with quartic coupling. Analyzing CFT data within the scope of $ε$- 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.
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.
We derive the geodesic equation for determining the Ryu-Takayanagi surface in $AdS_3$ deformed by single trace $μT \bar T + \varepsilon_+ J \bar T + \varepsilon_- T \bar J$ deformation for generic values of $(μ, \varepsilon_+, \varepsilon_-)$ 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 $(μ, \varepsilon_+, \varepsilon_-)$ parameter space. We discuss the matching at leading order in small $(μ, \varepsilon_+, \varepsilon_-)$ 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.
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.
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 $CFT_2$.
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.
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.
We compute the Hagedorn temperature of $μT \bar T + \varepsilon_+ J \bar T + \varepsilon_-T \bar J$ 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 $μ$, $\varepsilon_+$, 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 $(μ, \varepsilon_+, \varepsilon_-)$ of the double trace deformed compact scalars.
We continue our study of string theory in a background that interpolates between $AdS_3$ in the infrared and a linear dilaton spacetime $R^{1,1}\times R_ϕ$ 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 $CFT_2$.
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.
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.
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.
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 $\mathbb{R}^{1,1}\times\mathbb{R}_ϕ$ 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.
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.
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{ö}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 $ρ$, temperature T and chemical potential $μ$. We find this solution upto second order in the dilaton anisotropy parameter $ρ$. 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 (${η\over s}\ge {1 \over 4 π} $) 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.