arXiv subjects

Daniel Kabat

Publications and source records attributed to Daniel Kabat.

At least 37 records · Page 2Linked to original sources

arXiv2019

Emergence of spacetime from the algebra of total modular Hamiltonians

We study the action of the CFT total modular Hamiltonian on the CFT representation of bulk fields with spin. In the vacuum of the CFT the total modular Hamiltonian acts as a bulk Lie derivative, reducing on the RT surface to a boost perpendicular to the RT surface. This enables us to reconstruct bulk fields with spin from the CFT. On fields with gauge redundancies the total modular Hamiltonian acts as a bulk Lie derivative together with a compensating bulk gauge (or diffeomorphism) transformation to restore the original gauge. We consider the Lie algebra generated by the total modular Hamiltonians of all spherical CFT subregions and define weakly-maximal Lie subalgebras as proper subalgebras containing a maximal set of total modular Hamiltonians. In a CFT state with a bulk dual, we show that the bulk spacetime parametrizes the space of these weakly-maximal Lie subalgebras. Each such weakly-maximal Lie subalgebra induces Lorentz transformations at a particular point in the bulk manifold. The bulk metric dual to a pure CFT state is invariant at each point under this transformation. This condition fixes the metric up to a conformal factor that can be computed from knowledge of the equation parametrizing extremal surfaces. This gives a holographic notion of the invariance of a pure CFT state under CFT modular flow.

hep-th↗

arXiv2018

Fluid analogs for rotating black holes

Fluid analog models for gravity are based on the idea that any spacetime geometry admits a reinterpretation in which space is thought of as a fluid flowing with a prescribed velocity. This fluid picture is a restatement of the ADM decomposition of the metric. Most of the literature has focused on flat spatial geometries and physical fluid flows, with a view toward possible laboratory realizations. Here we relax these conditions and consider fluid flows on curved and time-dependent spatial geometries, as a way of understanding and visualizing solutions to general relativity. We illustrate the utility of the approach with rotating black holes. For the Kerr black hole we develop a fluid description based on Doran coordinates. For spinning BTZ black holes we develop two different fluid descriptions. One involves static conical spatial slices, with the fluid orbiting the tip of the cone. The other resembles a cosmology, with the fluid flowing on a time-dependent cylindrical geometry.

gr-qc↗

arXiv2018

Does boundary quantum mechanics imply quantum mechanics in the bulk?

Perturbative bulk reconstruction in AdS/CFT starts by representing a free bulk field $ϕ^{(0)}$ as a smeared operator in the CFT. A series of $1/N$ corrections must be added to $ϕ^{(0)}$ to represent an interacting bulk field $ϕ$. These corrections have been determined in the literature from several points of view. Here we develop a new perspective. We show that correlation functions involving $ϕ^{(0)}$ suffer from ambiguities due to analytic continuation. As a result $ϕ^{(0)}$ fails to be a well-defined linear operator in the CFT. This means bulk reconstruction can be understood as a procedure for building up well-defined operators in the CFT which thereby singles out the interacting field $ϕ$. We further propose that the difficulty with defining $ϕ^{(0)}$ as a linear operator can be re-interpreted as a breakdown of associativity. Presumably $ϕ^{(0)}$ can only be corrected to become an associative operator in perturbation theory. This suggests that quantum mechanics in the bulk is only valid in perturbation theory around a semiclassical bulk geometry.

hep-th↗

arXiv2017

Local bulk physics from intersecting modular Hamiltonians

We show that bulk quantities localized on a minimal surface homologous to a boundary region correspond in the CFT to operators that commute with the modular Hamiltonian associated with the boundary region. If two such minimal surfaces intersect at a point in the bulk then CFT operators which commute with both extended modular Hamiltonians must be localized at the intersection point. We use this to construct local bulk operators purely from CFT considerations, without knowing the bulk metric, using intersecting modular Hamiltonians. For conformal field theories at zero and finite temperature the appropriate modular Hamiltonians are known explicitly and we recover known expressions for local bulk observables.

hep-th↗

arXiv2016

Locality, bulk equations of motion and the conformal bootstrap

We develop an approach to construct local bulk operators in a CFT to order $1/N^2$. Since 4-point functions are not fixed by conformal invariance we use the OPE to categorize possible forms for a bulk operator. Using previous results on 3-point functions we construct a local bulk operator in each OPE channel. We then impose the condition that the bulk operators constructed in different channels agree, and hence give rise to a well-defined bulk operator. We refer to this condition as the "bulk bootstrap." We argue and explicitly show in some examples that the bulk bootstrap leads to some of the same results as the regular conformal bootstrap. In fact the bulk bootstrap provides an easier way to determine some CFT data, since it does not require knowing the form of the conformal blocks. This analysis clarifies previous results on the relation between bulk locality and the bootstrap for theories with a $1/N$ expansion, and it identifies a simple and direct way in which OPE coefficients and anomalous dimensions determine the bulk equations of motion to order $1/N^2$.

hep-th↗

arXiv2016

Asymmetric interiors for small black holes

We develop the representation of infalling observers and bulk fields in the CFT as a way to understand the black hole interior in AdS. We first discuss properties of CFT states which are dual to black holes. We then show that in the presence of a Killing horizon bulk fields can be decomposed into pieces we call ingoing and outgoing. The ingoing field admits a simple operator representation in the CFT, even inside a small black hole at late times, which leads to a simple CFT description of infalling geodesics. This means classical infalling observers will experience the classical geometry in the interior. The outgoing piece of the field is more subtle. In an eternal two-sided geometry it can be represented as an operator on the left CFT. In a stable one-sided geometry it can be described using entanglement via the PR construction. But in an evaporating black hole trans-horizon entanglement breaks down at the Page time, which means that for old black holes the PR construction fails and the outgoing field does not see local geometry. This picture of the interior allows the CFT to reconcile unitary Hawking evaporation with the classical experience of infalling observers.

hep-th↗

arXiv2015

Bulk equations of motion from CFT correlators

To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk microcausality. This requires adding an infinite tower of smeared higher-dimension double-trace operators to the CFT definition of a bulk field, with coefficients that we explicitly compute. By summing the contribution of the higher-dimension operators we derive the equations of motion satisfied by these uplifted CFT operators and show that we precisely recover the expected bulk equations of motion. We exhibit the freedom in the CFT construction which corresponds to bulk field redefinitions.

hep-th↗

arXiv2014

Finite N and the failure of bulk locality: Black holes in AdS/CFT

We consider bulk quantum fields in AdS/CFT in the background of an eternal black hole. We show that for black holes with finite entropy, correlation functions of semiclassical bulk operators close to the horizon deviate from their semiclassical value and are ill-defined inside the horizon. This is due to the large-time behavior of correlators in a unitary CFT, and means the region near and inside the horizon receives corrections. We give a prescription for modifying the definition of a bulk field in a black hole background, such that one can still define operators that mimic the inside of the horizon, but at the price of violating microcausality. For supergravity fields we find that commutators at spacelike separation generically ~ exp(-S/2). Similar results hold for stable black holes that form in collapse. The general lesson may be that a small amount of non-locality, even over arbitrarily large spacelike distances, is an essential aspect of non-perturbative quantum gravity.

hep-th↗

arXiv2014

Decoding the hologram: Scalar fields interacting with gravity

We construct smeared CFT operators which represent a scalar field in AdS interacting with gravity. The guiding principle is micro-causality: scalar fields should commute with themselves at spacelike separation. To O(1/N) we show that a correct and convenient criterion for constructing the appropriate CFT operators is to demand micro-causality in a three-point function with a boundary Weyl tensor and another boundary scalar. The resulting bulk observables transform in the correct way under AdS isometries and commute with boundary scalar operators at spacelike separation, even in the presence of metric perturbations.

hep-th↗

arXiv2013

On three dimensions as the preferred dimensionality of space via the Brandenberger-Vafa mechanism

In previous work it was shown that, in accord with the Brandenberger-Vafa mechanism, three is the maximum number of spatial dimensions that can grow large cosmologically from an initial thermal fluctuation. Here we complement that work by considering the possibility of successive fluctuations. Suppose an initial fluctuation causes at least one dimension to grow, and suppose successive fluctuations occur on timescales of order alpha'^{1/2}. If the string coupling is sufficiently large, we show that such fluctuations are likely to push a three-dimensional subspace to large volume where winding modes annihilate. In this setting three is the preferred number of large dimensions. Although encouraging, a more careful study of the dynamics and statistics of fluctuations is needed to assess the likelihood of our assumptions.

hep-th↗

arXiv2013

On the Mutual Information in Hawking Radiation

We compute the mutual information of two Hawking particles emitted consecutively by an evaporating black hole. Following Page, we find that the mutual information is of order exp(-S) where S is the entropy of the black hole. We speculate on implications for black hole unitarity, in particular on a possible failure of locality at large distances.

hep-th↗

arXiv2013

Black Hole Formation in Fuzzy Sphere Collapse

We study the collapse of a fuzzy sphere, that is a spherical membrane built out of D0-branes, in the BFSS model. At weak coupling, as the sphere shrinks, open strings are produced. If the initial radius is large then open string production is not important and the sphere behaves classically. At intermediate initial radius the back-reaction from open string production is important but the fuzzy sphere retains its identity. At small initial radius the sphere collapses to form a black hole. The crossover between the later two regimes is smooth and occurs at the correspondence point of Horowitz and Polchinski.

hep-th↗

arXiv2013

Black Hole Formation at the Correspondence Point

We study the process of bound state formation in a D-brane collision. We consider two mechanisms for bound state formation. The first, operative at weak coupling in the worldvolume gauge theory, is pair creation of W-bosons. The second, operative at strong coupling, corresponds to formation of a large black hole in the dual supergravity. These two processes agree qualitatively at intermediate coupling, in accord with the correspondence principle of Horowitz and Polchinski. We show that the size of the bound state and timescale for formation of a bound state agree at the correspondence point. The timescale involves matching a parametric resonance in the gauge theory to a quasinormal mode in supergravity.

hep-th↗

arXiv2013

CFT representation of interacting bulk gauge fields in AdS

We develop the representation of interacting bulk gauge fields and charged scalar matter in AdS in terms of non-local observables in the dual CFT. We work in holographic gauge in the bulk, A_z = 0. The correct statement of micro-causality in holographic gauge is somewhat subtle, so we first discuss it from the bulk point of view. We then show that in the 1/N expansion CFT correlators can be lifted to obtain bulk correlation functions which satisfy micro-causality. This requires adding an infinite tower of higher-dimension multi-trace operators to the CFT definition of a bulk observable. For conserved currents the Ward identities in the CFT prevent the construction of truly local bulk operators (i.e. operators that commute at spacelike separation with everything), however the resulting non-local commutators are exactly those required by the bulk Gauss constraint. In contrast a CFT which only has non-conserved currents can be lifted to a bulk theory which is truly local. Although our explicit calculations are for gauge theory, similar statements should hold for gravity.

hep-th↗

arXiv2012

Cosmic string interactions induced by gauge and scalar fields

We study the interaction between two parallel cosmic strings induced by gauge fields and by scalar fields with non-minimal couplings to curvature. For small deficit angles the gauge field behaves like a collection of non-minimal scalars with a specific value for the non-minimal coupling. We check this equivalence by computing the interaction energy between strings at first order in the deficit angles. This result provides another physical context for the "contact terms" which play an important role in the renormalization of black hole entropy due to a spin-1 field.

hep-th↗

arXiv2012

Holographic representation of bulk fields with spin in AdS/CFT

We develop the representation of bulk fields with spin one and spin two in anti-de Sitter space, as non-local observables in the dual CFT. Working in holographic gauge in the bulk, at leading order in 1/N bulk gauge fields are obtained by smearing boundary currents over a sphere on the complexified boundary, while linearized metric fluctuations are obtained by smearing the boundary stress tensor over a ball. This representation respects AdS covariance up to a compensating gauge transformation. We also consider massive vector fields, where the bulk field is obtained by smearing a non-conserved current. We compute bulk two-point functions and show that bulk locality is respected. We show how to include interactions of massive vectors using 1/N perturbation theory, and we comment on the issue of general backgrounds.

hep-th↗

arXiv2011

Edges and Diffractive Effects in Casimir Energies

The prototypical Casimir effect arises when a scalar field is confined between parallel Dirichlet boundaries. We study corrections to this when the boundaries themselves have apertures and edges. We consider several geometries: a single plate with a slit in it, perpendicular plates separated by a gap, and two parallel plates, one of which has a long slit of large width, related to the case of one plate being semi-infinite. We develop a general formalism for studying such problems, based on the wavefunctional for the field in the gap between the plates. This formalism leads to a lower dimensional theory defined on the open regions of the plates or boundaries. The Casimir energy is then given in terms of the determinant of the nonlocal differential operator which defines the lower dimensional theory. We develop perturbative methods for computing these determinants. Our results are in good agreement with known results based on Monte Carlo simulations. The method is well suited to isolating the diffractive contributions to the Casimir energy.

hep-th↗

arXiv2011

Thermal diffractive corrections to Casimir energies

We study the interplay of thermal and diffractive effects in Casimir energies. We consider plates with edges, oriented either parallel or perpendicular to each other, as well as a single plate with a slit. We compute the Casimir energy at finite temperature using a formalism in which the diffractive effects are encoded in a lower dimensional non-local field theory that lives in the gap between the plates. The formalism allows for a clean separation between direct or geometric effects and diffractive effects, and makes an analytic derivation of the temperature dependence of the free energy possible. At low temperatures, with Dirichlet boundary conditions on the plates, we find that diffractive effects make a correction to the free energy which scales as T^6 for perpendicular plates, as T^4 for slits, and as T^4 log T for parallel plates.

hep-th↗