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We construct a holographic map that reconstructs massless fields (scalars, Maxwell field \& Fierz-Pauli field) in half-Minkowski spacetime in $d+1$ dimensions terms of smeared primary operators in a large $N$ factorizable CFT in $\mathbb{R}^{d-1,1}$ spacetime dimensions. This map is based on a Weyl (rescaling) transformation from the Poincar\'e wedge of AdS to the Minkowski half-space; and on the HKLL smearing function, which reconstructs local bulk operators in the Poincar\'e AdS in terms of smeared operators on the conformal boundary of the Poincar\'e wedge. The massless scalar field is reconstructed up to the level of two-point functions, while the Maxwell field and massless spin-2 fields are reconstructed at the level of the one-point function. We also discuss potential ways the map can be generalized to higher dimensions, and to the full Minkowski space., Comment: Updated bibliography, Updated discussion section, 20 pages, 2 figures

Quantum complexity has already shed light on CFT states dual to bulk geometries containing spacelike singularities \cite{Barbon:2015ria, Bolognesi:2018ion, Caputa:2021pad}. In this work, we turn our attention to quantum complexity of CFT/quantum gravity states dual to bulk geometries with a naked timelike singularity. The appearance of naked timelike singularities in semiclassical gravity is allowed in string theory, particularly in the context of holography, so long as they satisfy the \emph{Gubser criterion} \cite{Gubser:2000nd, Gursoy:2008za}. In this work, we use holographic complexity as a probe on geometries containing naked timelike singularities and explore potential relation to the Gubser criterion for detecting allowable naked timelike singularities. We study three specific cases, namely the negative mass Schwarzschild-AdS spacetime, the timelike Kasner-AdS \cite{Ren:2016xhb} and Einstein-dilaton system \cite{Ren:2019lgw}. The first two cases are outright ruled out by the Gubser criterion while the third case is more subtle - according to the Gubser criterion the singularity switches from forbidden to admissible as the parameter $\alpha$ is dialed in the range $[0,1]$ across the transition point at $\alpha = 1/\sqrt{3}$. We probe all three geometries using two holographic complexity prescriptions, namely CA and CV. For the case of the negative mass SAdS and timelike Kasner-AdS$_4$ the complexities display no sign of pathology (both receive finite contribution from the naked singularity). For the Einstein-Dilaton case, action-complexity does display a sharp transition from physical positive values to patholgical negative divergent values (arising from the singularity) as one transcends the Gubser bound. Our study suggests that neither action-complexity (CA) nor volume-complexity (CV) can serve as a sensitive tool to investigate (naked) timelike singularities., Comment: 37 pages, 3 figures, Version accepted for publication in JHEP

This work is an extension of our previous work [1] where we exploited holography to compute the complexity characteristics of Little String Theory (LST), a nonlocal, nongravitational field theory which flows to a local 2d CFT in the IR under RG via an integrable irrelevant (TT) deformation. Here we look at the more general LST obtained by UV deforming the 2d CFT by incorporating Lorentz violating irrelevant JT and TJ deformations on top of TT deformation, in an effort to capture the novel signatures of Lorentz violation (on top of nonlocality) on quantum complexity. In anticipation of the fact that the dual field theory is Lorentz violating, we compute the volume complexity in two different Lorentz frames and the comparison is drawn between the results. It turns out that for this system the nonlocality and Lorentz violation effects are inextricably intertwined in the UV divergence structure of the quantum complexity. The coefficients of the divergences carry the signature of Lorentz boost violation. We also compute the subregion complexity which displays a (Hagedorn) phase transition with the transition point being the same as that for the phase transition of entanglement entropy [2]. These new results are consistent with our previous work [1]. Null warped AdS3 is treated as an interesting special case., Comment: 64 pages, 8 figures, accepted for publication in JHEP

Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS$_3$ spacetimes, thereby expanding the scope of holography beyond asymptotically AdS spacetimes. Here we investigate WCFT$_2$\,s using \emph{circuit complexity} as a tool. First we compute the holographic volume complexity (CV) which displays a linear UV divergence structure, more akin to that of a local CFT$_2$ and has a very complicated dependence on the Virasoro central charge $c$ and the $U(1)$ Kac-Moody level parameter $k$. Next we consider circuit complexity based on Virasoro-Kac-Moody symmetry gates where the complexity functional is the geometric (group) action on coadjoint orbits of the Virasoro-Kac-Moody group. We consider a special solution to extremization equations for which complexity scales linearly with ``time''. In the semiclassical limit (large $c,k$, while $c/k$ remains finite and small) both the holographic volume complexity and circuit complexity scales linearly with $k$., Comment: 34 pages, New references added; revised discussions of Virasoro-Kac-Moody circuits in section 3 although the final conclusions remain unchanged; updated discussion of complexity for warped conformal field theory. Version accepted for publication in EPJC

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

We perform a comparative study of the time dependence of the holographic quantum complexity of some space like singular bulk gravitational backgrounds. This is done by considering the two available notions of complexity, one that relates it to the maximal spatial volume and the other that relates it to the classical action of the Wheeler-de Witt patch. We calculate and compare the leading and the next to leading terms and find some universal features. The complexity decreases towards the singularity for both definitions, for all types of singularities studied. In addition the leading terms have the same quantitative behavior for both definitions in restricted number of cases and the behaviour itself is different for different singular backgrounds. The quantitative details of the next to leading terms, such as their specific form of time dependence, are found not to be universal. They vary between the different cases and between the different bulk definitions of complexity. We also address some technical points inherent to the calculation., Comment: 24 pages, 6 figures. v2: minor corrections

Most of the literature in the \emph{bulk reconstruction program} in holography focuses on recovering local bulk operators propagating on a quasilocal bulk geometry and the knowledge of the bulk geometry is always assumed or guessed. The fundamental problem of the bulk reconstruction program, which is \emph{recovering the bulk background geometry (metric)} from the boundary CFT state is still outstanding. In this work, we formulate a recipe to extract the bulk metric itself from the boundary state, specifically, the modular Hamiltonian information of spherical subregions in the boundary. Our recipe exploits the recent construction of Kabat and Lifschytz \cite{Kabat:2017mun} to first compute the bulk two point function of scalar fields directly in the CFT without knowledge of the bulk metric or the equations of motion, and then to take a large scaling dimension limit (WKB) to extract the geodesic distance between two close points in the bulk i.e. the metric. As a proof of principle, we consider three dimensional bulk and selected CFT states such as the vacuum and the thermofield double states. We show that they indeed reproduce the pure AdS and the regions outside the Rindler wedge and the BTZ black hole \emph{up to a rigid conformal factor}. Since our approach does not rely on symmetry properties of the CFT state, it can be applied to reconstruct asymptotically AdS geometries dual to arbitrary general CFT states provided the modular Hamiltonian is available. We discuss several obvious extensions to the case of higher spacetime dimensions as well as some future applications, in particular, for constructing metric beyond the causal wedge of a boundary region. In the process, we also extend the construction of \cite{Kabat:2017mun} to incorporate the first order perturbative locality for AdS scalars., Comment: 16+4 pages, 3 figures; v2: some clarifications and references added; v3: more clarifications added. Published version

We outline a holographic recipe to reconstruct $\alpha'$ corrections to AdS (quantum) gravity from an underlying CFT in the strictly planar limit ($N\rightarrow\infty$). Assuming that the boundary CFT can be solved in principle to all orders of the 't Hooft coupling $\lambda$, for scalar primary operators, the $\lambda^{-1}$ expansion of the conformal dimensions can be mapped to higher curvature corrections of the dual bulk scalar field action. Furthermore, for the metric pertubations in the bulk, the AdS/CFT operator-field isomorphism forces these corrections to be of the Lovelock type. We demonstrate this by reconstructing the coefficient of the leading Lovelock correction, aka the Gauss-Bonnet term in a bulk AdS gravity action using the expression of stress-tensor two-point function up to sub-leading order in $\lambda^{-1}$., Comment: 19 pages, typos corrected, published version (journal version title is different)

In this paper we extend the HKLL holographic smearing function method to reconstruct (quasi)local AdS bulk scalar observables in the background of a large AdS black hole formed by null shell collapse (a "pure state" black hole), from the dual CFT which is undergoing a sudden quench. In particular, we probe the near horizon and sub-horizon bulk locality. First we construct local bulk operators from the CFT in the leading semiclassical limit, $N\rightarrow\infty$. Then we look at effects due to the finiteness of $N$, where we propose a suitable coarse-graining prescription involving early and late time cut-offs to define semiclassical bulk observables which are approximately local; their departure from locality being non-perturbatively small in $N$. Our results have important implications on the black hole information problem., Comment: 41 pages, 11 figures, Typos fixed, Minor changes to Discussions and Outlook sections