We study modular Hamiltonians corresponding to the vacuum state for deformed half-spaces in relativistic quantum field theories on $$ {\mathrm{\mathbb{R}}}^{1,d-1} . show that addition usual boost generator, there is a contribution Hamiltonian at first order shape deformation, proportional integral of null components stress tensor along Rindler horizon. use this fact with monotonicity relative entropy prove averaged energy condition Minkowski space-time. This subsequently gives new proof...

We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. model the microstates of terms field theory living on end world brane behind horizon, and allow this to itself have holographic dual geometry. This geometry is also since entanglement leaves them mixed state. "inception hole" can be purified by through wormhole system which naturally identified external radiation, giving realization ER=EPR scenario. In context, we propose extension...

We study the transport properties of topological insulators, encoding them in a generating functional gauge and gravitational sources. Much our focus is on simple example free massive Dirac fermion, so-called Chern insulator, especially $2+1$ dimensions. In such cases, when parity time-reversal symmetry are broken, it necessary to consider sources include frame an independent spin connection with torsion. dimensions, simplest parity-odd response Hall viscosity. compute viscosity insulator...

A bstract We study the quantum complexity of time evolution in large- N chaotic systems, with SYK model as our main example. This is expected to increase linearly for exponential prior saturating at its maximum value, and related length minimal geodesics on manifold unitary operators that act Hilbert space. Using Euler-Arnold formalism, we demonstrate there always a geodesic between identity operator e −iHt whose grows time. until an obstruction minimality, after which it can fail be minimum...

In this paper, we demonstrate the emergence of nonlinear gravitational equations directly from physics a broad class conformal field theories. We consider CFT excited states defined by adding sources for scalar primary or stress tensor operators to Euclidean path integral defining vacuum state. For these states, show that up second order in sources, entanglement entropy all ball-shaped regions can always be represented geometrically (via Ryu-Takayanagi formula) an asymptotically AdS...

A bstract The reflected entropy S R ( : B ) of a density matrix ρ AB is bipartite correlation measure lower-bounded by the quantum mutual information I ). In holographic states satisfying extremal surface formula, where related to area entanglement wedge cross-section, there often an order- N 2 gap between and . We provide information-theoretic interpretation this observing that − fidelity particular Markov recovery problem impossible in any state whose cross-section has nonempty boundary;...

A bstract We use the SYK family of models with N Majorana fermions to study complexity time evolution, formulated as shortest geodesic length on unitary group manifold between identity and evolution operator, in free, integrable, chaotic systems. Initially, follows trajectory, hence grows linearly time. how this linear growth is eventually truncated by appearance accumulation conjugate points, which signal presence shorter geodesics intersecting trajectory. By explicitly locating such...

We study universal features in the shape dependence of entanglement entropy vacuum state a conformal field theory (CFT) on $\mathbb{R}^{1,d-1}$. consider across deformed planar or spherical entangling surface terms perturbative expansion infinitesimal deformation. In particular, we focus second order term this expansion, known as density. This quantity is to be non-positive by strong-subadditivity property. show from purely calculation that non-local part density any CFT universal, and...

We study the response of a class topological systems to electromagnetic and gravitational sources, including torsion curvature. By using technology anomaly polynomials, we derive parity-odd massive Dirac fermion in $d=2+1$ $d=4+1$, which provides simple model for insulator. discuss covariant anomalies corresponding edge states, from Callan-Harvey anomaly-inflow, as well Hamiltonian spectral flow point view. also applicability our results other such Weyl semi-metals. Finally, dimensional...

An important conjecture in knot theory relates the large-N, double scaling limit of colored Jones polynomial JK,N(q) a K to hyperbolic volume complement, Vol(K). A less studied question is whether Vol(K) can be recovered directly from original (N=2). In this report we use deep neural network approximate polynomial. Our robust and correctly predicts with 97.6% accuracy when training on 10% data. This points existence more direct connection between

A bstract We study shape-deformations of the entanglement entropy and modular Hamiltonian for an arbitrary subregion state (with a smooth dual geometry) in holographic conformal field theory. More precisely, we double-deformation comprising shape deformation together with deformation, where latter corresponds to small change bulk geometry. Using purely gravitational identity from Hollands-Iyer-Wald formalism assumption equality between boundary flows original, undeformed subregion, rewrite...

We consider the Wilson-Polchinski exact renormalization group (RG) applied to generating functional of single-trace operators at a free-fixed point in $d=2+1$ dimensions. By exploiting rich symmetry structure free-field theory, we study geometric nature RG equations and associated Ward identities. The geometry, as expected, is holographic, with anti--de Sitter spacetime emerging correspondent fixed points. field theory construction gives us particular vector bundle over $d+1$-dimensional...

A bstract We consider states of holographic conformal field theories constructed by adding sources for local operators in the Euclidean path integral, with aim investigating extent to which arbitrary bulk coherent can be represented such path-integrals CFT. construct associated dual Lorentzian spacetimes perturbatively sources. Extending earlier work, we provide explicit formulae fields first order general scalar and metric perturbations dimensions. check results holographically computing...

We consider Chern-Simons theory for gauge group $G$ at level $k$ on 3-manifolds $M_n$ with boundary consisting of $n$ topologically linked tori. The Euclidean path integral defines a quantum state the boundary, in $n$-fold tensor product torus Hilbert space. focus case where is link-complement some $n$-component link inside three-sphere $S^3$. entanglement entropies resulting states define framing-independent invariants which are sensitive to topology chosen link. For Abelian ($G= U(1)_k$)...

A bstract For any state in a D -dimensional Hilbert space with choice of basis, one can define discrete version the Wigner function — quasi-probability distribution which represents on phase space. The can, general, take negative values, and amount negativity has an operational meaning as resource for quantum computation. In this note, we study growth generic initial under time evolution chaotic Hamiltonians. We introduce Krylov-Wigner function, i.e., defined respect to Krylov basis (with...

In this paper, we revisit scalar field theories in $d$ space-time dimensions possessing $U(N)$ global symmetry. Following our recent work [1], consider the generating function of correlation functions all $U(N)$-invariant, single-trace operators at free-fixed point. The exact renormalization group equations are cast as Hamilton radial evolution a model one higher dimension, case ${\mathrm{AdS}}_{d+1}$. geometry associated with is seen to emerge naturally out infinite jet bundle corresponding...

We study the entanglement entropy between (possibly distinct) topological phases across an interface using Abelian Chern-Simons description with boundary conditions (TBCs) at interface. From a microscopic point of view, these TBCs correspond to turning on particular gapping interactions edge modes However, in studying continuum description, we must confront problem non-factorization Hilbert space, which is standard property gauge theories. carefully define by extended space construction...

We study the Page curve and island rule for black holes evaporating into gravitating baths, with an eye towards establishing a connection ER=EPR proposal. consider several models of two entangled 2d in Jackiw-Teitelboim (JT) gravity negative cosmological constant. The first, "doubled PSSY," model is one which have end-of-the-world (ETW) branes flavour degree freedom. highly states this freedom find entanglement-induced Hawking-Page-like transition from geometry disconnected to pair connected...

A bstract We discuss a one-parameter family of states in two-dimensional holographic conformal field theories which are constructed via the Euclidean path integral an effective theory on hyperbolic slices dual bulk geometry. The question is CFT flowed under $$ T\overline{T} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> deformation, “folds” boundary towards time-reflection symmetric slice. propose that...

A bstract We study the quantum error correction properties of black hole interior in a toy model for an evaporating hole: Jackiw-Teitelboim gravity entangled with non-gravitational bath. After Page time, degrees freedom this system are encoded bath Hilbert space. use gravitational path integral to show that density matrix is correctable against action operations on which (i) do not have prior access details microstates, and (ii) large, negative coherent information respect maximally mixed...

A bstract We study the multi-party entanglement structure of states in Chern-Simons theory created by performing path integral on 3-manifolds with linked torus boundaries, called link complements. For gauge group SU(2), wavefunctions these (in a particular basis) are colored Jones polynomials corresponding links. first review case U(1) where stabilizer states, fact we use to re-derive an explicit formula for entropy across general bipartition. then present following results SU(2) theory: (i)...

A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well the metastability electroweak vacuum, can all be understood problems This suggests a statistical physics approach, based on landscape string theory. In this paper we present dynamical selection mechanism for hospitable vacua search optimization. Instead focusing late-time, stationary probability distributions different vacua, are interested in approach to equilibrium....

Entanglement entropy for spatial subregions is difficult to define in string theory because of the extended nature strings. Here we propose a definition Bosonic open strings using framework field theory. The key difference (compared ordinary quantum theory) that subregion chosen inside Cauchy surface "space configurations". We first present simple calculation this entanglement free light-cone theory, ignoring subtleties related factorization Hilbert space. reproduce answer expected from an...

By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically anti--de Sitter (AdS) spacetime computes entanglement entropies ball-shaped regions in conformal field theory using generalized Ryu-Takayanagi formula up second order state deformations around vacuum, then satisfies correct gravitational equations motion AdS background. (ii) The holographic dual entropy theories gravity is...