We study holographic entanglement entropy in dS/CFT and introduce time-like entanglement entropy in CFTs. Both of them take complex values in general and are related with each other via an analytical continuation. We argue that they are correctly understood as pseudo entropy. We find that the imaginary part of pseudo entropy implies an emergence of time in dS/CFT.

We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space.

We model the Hayden--Preskill (HP) information recovery protocol in 2d CFTs via local joining quenches. Euclidean path integrals with slits prepare the HP subsystems: the message $M$, its reference $N$, the Page-time black hole $B$, the early radiation $E$, and the late radiation $R$; the remaining black hole after emitting $R$ is denoted as $B'$. The single-slit geometry provides an analytically tractable toy model, while the bounded-slit geometry more closely captures the HP setup. In the free Dirac fermion 2d CFT, the mutual information $I(N\!:\!B')$ shows quasi-particle dynamics with partial or full revivals, whereas that in holographic 2d CFTs, which are expected to be maximally chaotic, exhibit sharp transitions: in the bounded-slit case, when the size of the late radiation becomes comparable to that of the reference $N$, $I(N\!:\!B')$ does vanish at late time, otherwise it remains finite. This contrast between free CFTs and holographic CFTs gives a clear characterization of the HP recovery threshold.

In this paper, we study the time-dependent dynamics of an end-of-the-world (EOW) brane in AdS with a scalar field localized on the brane. We mainly studied several aspects of holography and cosmology. Standard requirements in the AdS$_{d+1}$/CFT$_d$ lead to a constraint on the conformal dimension in the dS$_d$/CFT$_{d-1}$. We also prove a time-like analog of g-theorem using the null energy condition in the context of AdS$_3$/BCFT$_2$. In the cosmological interpretation, we rewrite the equation of motion of the brane as a Friedman-like equation, which enables us to consider its dynamics in analogy with the ordinal cosmology. And then we classify all possible solutions of the brane when the potential takes a constant value. We find that our brane cosmology model can describe a process of creating a universe via a big-bang. Additionally, we show that when the brane is close to a hyperplane, its effective action is given by a Liouville gravity with a scalar field matter. Finally, we also obtain brane solutions with boost symmetry, which are obtained by analytical continuation of Euclidean branes with a torus topology.

In this paper we construct CFT states describing a putative holographic dual to local excitations in the three-dimensional de Sitter space (dS), called the bulk local states. We find that the conjugation operation in dS$_3/$CFT$_2$ is notably different from that in AdS$_3/$CFT$_2$. This requires us to combine two bulk local states constructed out of different primary states in a CPT-invariant way. This analysis explains why Green's functions in the dS Euclidean vacuum cannot simply be obtained from the Wick rotation of those in AdS. We also argue that this characteristic feature explains the emergence of a time coordinate from the dual Euclidean CFT. We show that the information metric for the quantum estimation of bulk coordinate values replicates the de Sitter space metric.

The black hole singularity plays a crucial role in formulating Hawking's information paradox. The global spacetime analysis may be reconciled with unitarity by imposing a final state boundary condition on the spacelike singularity. Motivated by the final state proposal, we explore the effect of final state projection in two dimensional conformal field theories. We calculate the time evolution under postselection by employing the real part of pseudo-entropy to estimate the amount of quantum entanglement averaged over histories between the initial and final states. We find that this quantity possesses a Page curve-like behavior.

We explore the reconstruction of bulk local states in three-dimensional flat spacetime (Flat$_3$) using states from two-dimensional Carrollian conformal field theories (CCFT$_2$), proposed as dual field theories in one lower dimension. For massive scalar-type bulk excitations, reconstruction is achieved through states in the induced representation. This method successfully reproduces the bulk massive scalar spectrum and the bulk-to-bulk propagator. Additionally, we identify a new flat limit from AdS$_3$ and dS$_3$ spacetimes, further validating our proposal for scalar reconstruction in Flat$_3$/CCFT$_2$.

In this paper we study various dynamical aspects of the AdS/BCFT correspondence in higher dimensions. We study properties of holographic stress energy tensor by analyzing the metric perturbation in the gravity dual. We also calculate the stress energy tensor for a locally excited state on a half plane in a free scalar CFT. Both of them satisfy a reflective boundary condition that is expected for any BCFTs. We also study the behavior of the scalar field perturbation in the AdS/BCFT setup and show that they also show complete reflections. Moreover, we find that the entanglement entropy of a BCFT computed from the AdS/BCFT matched with that calculated from the Island formula, which supports the Island/BCFT correspondence in higher dimensions. Finally we show how we can calculate one point functions in a BCFT in our gravity dual.

We consider the evolution of entanglement entropy in a two-dimensional conformal field theory with a holographic dual. Specifically, we are interested in a class of excited states produced by a combination of pure-state (local operator) and mixed-state local quenches. We employ a method that allows us to determine the full time evolution analytically. While a single insertion of a local operator gives rise to a logarithmic time profile of entanglement entropy relative to the vacuum, we find that this growth is heavily suppressed in the presence of a mixed-state quench, reducing it to a time-independent constant bump. The degree of suppression depends on the relative position of the quenches as well as the ratio of regularization parameters associated with the quenches. This work sheds light on the interesting properties of gravitational scattering involving black holes.

In this paper we study a connection between Jackiw-Teitelboim (JT) gravity on two-dimensional anti de-Sitter spaces and a semiclassical limit of c<1 two-dimensional string theory. The world-sheet theory of the latter consists of a space-like Liouville CFT coupled to a non-rational CFT defined by a time-like Liouville CFT. We show that their actions, disk partition functions and annulus amplitudes perfectly agree with each other, where the presence of boundary terms plays a crucial role. We also reproduce the boundary Schwarzian theory from the Liouville theory description. Then, we identify a matrix model dual of our two-dimensional string theory with a specific time-dependent background in $c=1$ matrix quantum mechanics. Finally, we also explain the corresponding relation for the two-dimensional de-Sitter JT gravity.

In this work, we develop a generalisation of the thermal entropy to complex inverse temperatures, which we call the thermal pseudo-entropy. We show that this quantity represents the pseudo-entropy of the transition matrix between Thermofield Double states at different times. We have studied its properties in various quantum mechanical setups, Schwarzian theory, Random Matrix Theories, and 2D CFTs, including symmetric orbifolds. Our findings indicate a close relationship between the averaged thermal pseudo-entropy and the spectral form factor, which is instrumental in distinguishing chaotic and integrable models. Moreover, we have observed a logarithmic scaling of this quantity in models with a continuous spectrum, with a universal coefficient that is sensitive to the scaling of the density of states near the edge of the spectrum. Lastly, we found the connection between the real and imaginary parts of the thermal pseudo-entropy through the Kramers-Kronig relations.

In this paper we propose a holographic duality for classical gravity on a three-dimensional de Sitter space. We first show that a pair of SU$(2)$ Chern-Simons gauge theories reproduces the classical partition function of Einstein gravity on a Euclidean de Sitter space, namely $\mathbb{S}^3$, when we take the limit where the level $k$ approaches $-2$. This implies that the CFT dual of gravity on a de Sitter space at the leading semi-classical order is given by an SU$(2)$ Wess-Zumino-Witten (WZW) model in the large central charge limit $k\to -2$. We give another evidence for this in the light of known holography for coset CFTs. We also present a higher spin gravity extension of our duality.

In this paper we study a connection between Jackiw-Teitelboim (JT) gravity on two-dimensional anti de-Sitter spaces and a semiclassical limit of c<1 two-dimensional string theory. The world-sheet theory of the latter consists of a space-like Liouville CFT coupled to a non-rational CFT defined by a time-like Liouville CFT. We show that their actions, disk partition functions and annulus amplitudes perfectly agree with each other, where the presence of boundary terms plays a crucial role. We also reproduce the boundary Schwarzian theory from the Liouville theory description. Then, we identify a matrix model dual of our two-dimensional string theory with a specific time-dependent background in $c=1$ matrix quantum mechanics. Finally, we also explain the corresponding relation for the two-dimensional de-Sitter JT gravity.

We show that strong subadditivity provides a simple derivation of the $g$-theorem for the boundary renormalization group flow in two-dimensional conformal field theories. We work out its holographic interpretation and also give a derivation of the $g$-theorem for the case of an interface in two-dimensional conformal field theories. We also geometrically confirm strong subadditivity for holographic duals of conformal field theories on manifolds with boundaries.

The Bethe lattice Ising model -- a classical model of statistical mechanics for the phase transition -- provides a novel and intuitive understanding of the prototypical relationship between tensor networks and Anti-de Sitter (AdS)/conformal field theory (CFT) correspondence. After analytically formulating a holographic renormalization group for the Bethe lattice model, we demonstrate the underlying mechanism and the exact scaling dimensions for the power-law decay of boundary spin correlations by introducing the relation between the lattice network and an effective Poincare metric on a unit disk. We compare the Bethe lattice model in the high-temperature region with a scalar field in AdS$_2$, and then discuss its more direct connection to the p-adic AdS/CFT. In addition, we find that the phase transition in the interior induces a crossover behavior of boundary spin correlations, depending on the depth of the corresponding correlation path.

In software development, developers frequently apply maintenance activities to the source code that change a few lines by a single commit. A good understanding of the characteristics of such small changes can support quality assurance approaches (e.g., automated program repair), as it is likely that small changes are addressing deficiencies in other changes; thus, understanding the reasons for creating small changes can help understand the types of errors introduced. Eventually, these reasons and the types of errors can be used to enhance quality assurance approaches for improving code quality. While prior studies used code churns to characterize and investigate the small changes, such a definition has a critical limitation. Specifically, it loses the information of changed tokens in a line. For example, this definition fails to distinguish the following two one-line changes: (1) changing a string literal to fix a displayed message and (2) changing a function call and adding a new parameter. These are definitely maintenance activities, but we deduce that researchers and practitioners are interested in supporting the latter change. To address this limitation, in this paper, we define micro commits, a type of small change based on changed tokens. Our goal is to quantify small changes using changed tokens. Changed tokens allow us to identify small changes more precisely. In fact, this token-level definition can distinguish the above example. We investigate defined micro commits in four OSS projects and understand their characteristics as the first empirical study on token-based micro commits. We find that micro commits mainly replace a single name or literal token, and micro commits are more likely used to fix bugs. Additionally, we propose the use of token-based information to support software engineering approaches in which very small changes significantly affect their effectiveness.

In this paper, we study the dynamics of end-of-the-world (EOW) branes in AdS with scalar fields localized on the branes as a new class of gravity duals of CFTs on manifolds with boundaries. This allows us to construct explicit solutions dual to boundary RG flows. We also obtain a variety of annulus-like or cone-like shaped EOW branes, which are not possible without the scalar field. We also present a gravity dual of a CFT on a strip with two different boundary conditions due to the scalar potential, where we find the confinement/deconfinement-like transition as a function of temperature and the scalar potential. Finally, we point out that this phase transition is closely related to the measurement-induced phase transition, via a Wick rotation.