arXiv subjects

Tatsuma Nishioka

Publications and source records attributed to Tatsuma Nishioka.

At least 37 records · Page 2Linked to original sources

arXiv2021

Topological pseudo entropy

We introduce a pseudo entropy extension of topological entanglement entropy called topological pseudo entropy. Various examples of the topological pseudo entropies are examined in three-dimensional Chern-Simons gauge theory with Wilson loop insertions. Partition functions with knotted Wilson loops are directly related to topological pseudo (Rényi) entropies. We also show that the pseudo entropy in a certain setup is equivalent to the interface entropy in two-dimensional conformal field theories (CFTs), and leverage the equivalence to calculate the pseudo entropies in particular examples. Furthermore, we define a pseudo entropy extension of the left-right entanglement entropy in two-dimensional boundary CFTs and derive a universal formula for a pair of arbitrary boundary states. As a byproduct, we find that the topological interface entropy for rational CFTs has a contribution identical to the topological entanglement entropy on a torus.

hep-th↗

arXiv2021

Free energy and defect $C$-theorem in free scalar theory

We describe conformal defects of $p$ dimensions in a free scalar theory on a $d$-dimensional flat space as boundary conditions on the conformally flat space $\mathbb{H}^{p+1}\times \mathbb{S}^{d-p-1}$. We classify two types of boundary conditions, Dirichlet type and Neumann type, on the boundary of the subspace $\mathbb{H}^{p+1}$ which correspond to the types of conformal defects in the free scalar theory. We find Dirichlet boundary conditions always exist while Neumann boundary conditions are allowed only for defects of lower codimensions. Our results match with a recent classification of the non-monodromy defects, showing Neumann boundary conditions are associated with non-trivial defects. We check this observation by calculating the difference of the free energies on $\mathbb{H}^{p+1}\times \mathbb{S}^{d-p-1}$ between Dirichlet and Neumann boundary conditions. We also examine the defect RG flows from Neumann to Dirichlet boundary conditions and provide more support for a conjectured $C$-theorem in defect CFTs.

hep-th↗

arXiv2021

Probing Hawking radiation through capacity of entanglement

We consider the capacity of entanglement in models related with the gravitational phase transitions. The capacity is labeled by the replica parameter which plays a similar role to the inverse temperature in thermodynamics. In the end of the world brane model of a radiating black hole the capacity has a peak around the Page time indicating the phase transition between replica wormhole geometries of different types of topology. Similarly, in a moving mirror model describing Hawking radiation the capacity typically shows a discontinuity when the dominant saddle switches between two phases, which can be seen as a formation of island regions. In either case we find the capacity can be an invaluable diagnostic for a black hole evaporation process.

hep-th↗

arXiv2020

Regge OPE blocks and light-ray operators

We consider the structure of the operator product expansion (OPE) in conformal field theory by employing the OPE block formalism. The OPE block acted on the vacuum is promoted to an operator and its implications are examined on a non-vacuum state. We demonstrate that the OPE block is dominated by a light-ray operator in the Regge limit, which reproduces precisely the Regge behavior of conformal blocks when used inside scalar four-point functions. Motivated by this observation, we propose a new form of the OPE block, called the light-ray channel OPE block that has a well-behaved expansion dominated by a light-ray operator in the Regge limit. We also show that the two OPE blocks have the same asymptotic form in the Regge limit and confirm the assertion that the Regge limit of a pair of spacelike-separated operators in a Minkowski patch is equivalent to the OPE limit of a pair of timelike-separated operators associated with the original pair in a different Minkowski patch.

hep-th↗

arXiv2020

Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories

We study the entropy associated with the Janus interface in a 4$d$ $\mathcal{N}=2$ superconformal field theory. With the entropy defined as the interface contribution to an entanglement entropy we show, under mild assumptions, that the Janus interface entropy is proportional to the geometric quantity called Calabi's diastasis on the space of $\mathcal{N}=2$ marginal couplings, confirming an earlier conjecture by two of the authors and generalizing a similar result in two dimensions. Our method is based on a CFT consideration that makes use of the Casini-Huerta-Myers conformal map from the flat space to the round sphere.

hep-th↗

arXiv2020

The gravity dual of Lorentzian OPE blocks

We consider the operator product expansion (OPE) structure of scalar primary operators in a generic Lorentzian CFT and its dual description in a gravitational theory with one extra dimension. The OPE can be decomposed into certain bi-local operators transforming as the irreducible representations under conformal group, called the OPE blocks. We show the OPE block is given by integrating a higher spin field along a geodesic in the Lorentzian AdS space-time when the two operators are space-like separated. When the two operators are time-like separated however, we find the OPE block has a peculiar representation where the dual gravitational theory is not defined on the AdS space-time but on a hyperboloid with an additional time coordinate and Minkowski space-time on its boundary. This differs from the surface Witten diagram proposal for the time-like OPE block, but in two dimensions we reproduce it consistently using a kinematical duality between a pair of time-like separated points and space-like ones.

hep-th↗

arXiv2019

Spinning conformal defects

We consider conformal defects with spins under the rotation group acting on the transverse directions. They are described in the embedding space formalism in a similar manner to spinning local operators, and their correlation functions with bulk and defect local operators are determined by the conformal symmetry. The operator product expansion (OPE) structure of spinning conformal defects is examined by decomposing it into the spinning defect OPE block that packages all the contribution from a conformal multiplet. The integral representation of the block derived in the shadow formalism is facilitated to deduce recursion relations for correlation functions of two spinning conformal defects. In simple cases, we construct spinning defect correlators by acting differential operators recursively on scalar defect correlators.

hep-th↗

arXiv2019

Entanglement entropy: holography and renormalization group

Entanglement entropy plays a variety of roles in quantum field theory, including the connections between quantum states and gravitation through the holographic principle. This article provides a review of entanglement entropy from a mixed viewpoint of field theory and holography. A set of basic methods for the computation is developed and illustrated with simple examples such as free theories and conformal field theories. The structures of the ultraviolet divergences and the universal parts are determined and compared with the holographic descriptions of entanglement entropy. The utility of quantum inequalities of entanglement are discussed and shown to derive the C-theorem that constrains renormalization group flows of quantum field theories in diverse dimensions.

hep-th↗

arXiv2018

Towards a $C$-theorem in defect CFT

We explore a $C$-theorem in defect conformal field theories (DCFTs) that unify all the known conjectures and theorems until now. We examine as a candidate $C$-function the additional contributions from conformal defects to the sphere free energy and the entanglement entropy across a sphere in a number of examples including holographic models. We find the two quantities are equivalent, when suitably regularized, for codimension-one defects (or boundaries), but differ by a universal constant term otherwise. Moreover, we find in a few field theoretic examples that the sphere free energy decreases but the entanglement entropy increases along a certain renormalization group (RG) flow triggered by a defect localized perturbation which is assumed to have a trivial IR fixed point without defects. We hence propose a $C$-theorem in DCFTs stating that the increment of the regularized sphere free energy due to the defect does not increase under any defect RG flow. We also provide a proof of our proposal in several holographic models of defect RG flows.

hep-th↗

arXiv2017

Operator product expansion for conformal defects

We study the operator product expansion (OPE) for scalar conformal defects of any codimension in CFT. The OPE for defects is decomposed into "defect OPE blocks", the irreducible representations of the conformal group, each of which packages the contribution from a primary operator and its descendants. We use the shadow formalism to deduce an integral representation of the defect OPE blocks. They are shown to obey a set of constraint equations that can be regarded as equations of motion for a scalar field propagating on the moduli space of the defects. By employing the Radon transform between the AdS space and the moduli space, we obtain a formula of constructing an AdS scalar field from the defect OPE block for a conformal defect of any codimension in a scalar representation of the conformal group, which turns out to be the Euclidean version of the HKLL formula. We also introduce a duality between conformal defects of different codimensions and prove the equivalence between the defect OPE block for codimension-two defects and the OPE block for a pair of local operators.

hep-th↗

arXiv2017

Supersymmetric Rényi Entropy and Defect Operators

We describe the defect operator interpretation of the supersymmetric Renyi entropies of superconformal field theories in three, four and five dimensions. The operators involved are supersymmetric codimension-two defects in an auxiliary Z_n gauge theory coupled to n copies of the SCFT. We compute the exact expectation values of such operators using localization, and compare the results to the supersymmetric Renyi entropy. The agreement between the two implies a relationship between the partition function on a squashed sphere and the one on a round sphere in the presence of defects.

hep-th↗

arXiv2016

A Holographic Proof of Rényi Entropic Inequalities

We prove Rényi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of Rényi entropies when the bulk is stable against any perturbation. Regarding the Rényi parameter as an inverse temperature, we reformulate the entropies in analogy with statistical mechanics, which provides us a concise interpretation of the inequalities as the positivities of entropy, energy and heat capacity. This analogy also makes clear a thermodynamic structure in deriving the holographic formula. As a by-product of the proof we obtain a holographic formula to calculate the quantum fluctuation of the modular Hamiltonian. A few examples of the capacity of entanglement are examined in detail.

hep-th↗

arXiv2016

The Edge of Entanglement: Getting the Boundary Right for Non-Minimally Coupled Scalar Fields

In entanglement computations for a free scalar field with coupling to background curvature, there is a boundary term in the modular Hamiltonian which must be correctly specified in order to get sensible results. We focus here on the entanglement in flat space across a planar interface and (in the case of conformal coupling) other geometries related to this one by Weyl rescaling of the metric. For these "half-space entanglement" computations, we give a new derivation of the boundary term and revisit how it clears up a number of puzzles in the literature, including mass corrections and twist operator dimensions. We also discuss how related boundary terms may show up in other field theories.

hep-th↗

arXiv2016

Renormalized Entanglement Entropy on Cylinder

We develop a framework of calculating entanglement entropy for non-conformal field theories with the use of the dilaton effective action. To illustrate it, we locate a theory on a cylinder $\mathbb{R} \times \mathbb{S}^{2}$ and compute entanglement entropy of a cap-like region perturbatively with respect to the mass for a free massive scalar field. A renormalized entanglement entropy (REE) is proposed to regularize the ultraviolet divergence on the cylinder. We find that the REE decreases monotonically both in the small and large mass regions as the mass increases. We confirm all of these behaviors by the numerical calculations, which further shows the monotonic decrease of the REE in the entire renormalization group flow.

hep-th↗

arXiv2015

Anomalies and Entanglement Entropy

We initiate a systematic study of entanglement and Renyi entropies in the presence of gauge and gravitational anomalies in even-dimensional quantum field theories. We argue that the mixed and gravitational anomalies are sensitive to boosts and obtain a closed form expression for their behavior under such transformations. Explicit constructions exhibiting the dependence of entanglement entropy on boosts is provided for theories on spacetimes with non-trivial magnetic fluxes and (or) non-vanishing Pontryagin classes.

hep-th↗

arXiv2015

Entanglement Entropy of Annulus in Three Dimensions

The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic mutual information in the CGLP background describing a gapped field theory. We discover four types of solutions as the minimal surfaces for the annulus and classify the phase diagrams by varying the inner and outer radii. In both cases, we find the mutual information satisfies the monotonicity dictated by the unitarity and decays exponentially fast as the gap scale is increased. We speculate this is a universal behavior in any gapped system.

hep-th↗

arXiv2014

Supersymmetric Rényi Entropy in Five Dimensions

We introduce supersymmetric Rényi entropies for $\mathcal{N}=1$ supersymmetric gauge theories in five dimensions. The matrix model representation is obtained using the localization method and the large-$N$ behavior is studied. The gravity dual is a supersymmetric charged topological AdS$_6$ black hole in the Romans $F(4)$ supergravity. The variation of the supersymmetric Rényi entropy due to the insertion of a BPS Wilson loop is computed. We find perfect agreements between the large-$N$ and the dual gravity computations both with and without the Wilson loop operator.

hep-th↗

arXiv2014

Holographic Interpolation between $a$ and $F$

An interpolating function $\tilde F$ between the $a$-anomaly coefficient in even dimensions and the free energy on an odd-dimensional sphere has been proposed recently and is conjectured to monotonically decrease along any renormalization group flow in continuous dimension $d$. We examine $\tilde F$ in the large-$N$ CFT's in $d$ dimensions holographically described by the Einstein-Hilbert gravity in the AdS$_{d+1}$ space. We show that $\tilde F$ is a smooth function of $d$ and correctly interpolates the $a$ coefficients and the free energies. The monotonicity of $\tilde F$ along an RG flow follows from the analytic continuation of the holographic $c$-theorem to continuous $d$, which completes the proof of the conjecture.

hep-th↗