The Lorentzian anti-de Sitter/conformal field theory correspondence implies a map between local operators in supergravity and nonlocal the CFT. By explicit computation we construct CFT which are dual to bulk fields semiclassical limit. is done for general dimension global, Poincar\'e Rindler coordinates. We find that can be taken have compact support region of complexified boundary whose size set by radial position. show at finite $N$ number independent commuting localized within volume...

We develop the representation of local bulk fields in AdS by non-local operators on boundary, working semiclassical limit and using AdS_2 as our main example. In global coordinates we show that boundary operator has support only at points which are spacelike separated from point. construct represent inserted behind horizon Poincare patch inside Rindler a two dimensional black hole. these respect locality comment generalization construction to higher holes.

Local operators in the bulk of AdS can be represented as smeared dual CFT. We show how to construct these observables by requiring that commute at spacelike separation. This extends our previous work taking interactions into account. Large-N factorization plays a key role construction. diagrammatically this procedure is related Feynman diagrams.

To gain insight into how bulk locality emerges from the holographic conformal field theory (CFT), we reformulate bulk-to-boundary map in as local a way possible. In previous work, carried out this program for Lorentzian anti-de Sitter (AdS), and showed support on boundary could always be reduced to compact region spacelike separated point. present work idea is extended complexified boundary, where spatial coordinates are continued imaginary values. This continuation enables us represent...

We construct smeared conformal field theory (CFT) operators which represent a scalar in anti--de Sitter (AdS) space interacting with gravity. The guiding principle is microcausality: fields should commute themselves at spacelike separation. To $\mathcal{O}(1/N)$ we show that correct and convenient criterion for constructing the appropriate CFT to demand microcausality three-point function boundary Weyl tensor another scalar. resulting bulk observables transform way under AdS isometries...

We consider low energy, nonrelativistic scattering of two Dirichlet zero-branes as an exercise in quantum mechanics. For weak string coupling and sufficiently small velocity, the dynamics is governed by effective U(2) gauge theory $0+1$ dimensions. At energies, D-brane can reliably probe distances much shorter than scale. The only length scale mechanics problem eleven-dimensional Planck length. This provides evidence for role scales weakly coupled type IIA strings.

We consider membranes of spherical topology in uncompactified Matrix theory.In general for large theory reproduces the classical membrane dynamics up to 1/N corrections; certain simple configurations, equations motion agree exactly at finite N. derive a formula one-loop potential between two finite-sized objects separations.Applied graviton interacting with round membrane, we show that agrees naive supergravity iV, but differs subleading orders The result is quite general: prove pair...

We study string dynamics in the early universe. Our motivation is proposal of Brandenberger and Vafa, that winding modes may play a key role decompactifying three spatial dimensions. model universe as homogeneous but anisotropic 9-torus filled with gas excited strings. adopt initial conditions which fix dilaton volume torus, otherwise assume all states are equally likely. evolution system both analytically numerically to determine late-time behavior. find that, although dynamical can indeed...

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

We develop the representation of interacting bulk gauge fields and charged scalar matter in AdS terms non-local observables dual CFT. work holographic bulk, A_z = 0. The correct statement micro-causality is somewhat subtle, so we first discuss it from point view. then show that 1/N expansion CFT correlators can be lifted to obtain correlation functions which satisfy micro-causality. This requires adding an infinite tower higher-dimension multi-trace operators definition a observable. For...

We show that a black hole surrounded by scalar dark matter develops hair. This is the generalization of phenomenon pointed out Jacobson, minimally coupled with non-trivial time dependence far away from would endow In our case, arises oscillation field non-zero mass. systematically explore profile around for different masses. small mass limit, has $1/r$ component at large radius $r$, consistent Jacobson's result. limit (with Compton wavelength order horizon or smaller), $1/r^{3/4}$ yielding...

We consider the thermal behavior of a large number matrix degrees freedom in planar limit. work <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>0</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:math> dimensions, with <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>D</c:mi></c:math> matrices, and use <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>1</e:mn><e:mo>/</e:mo><e:mi>D</e:mi></e:math> as an expansion parameter....

We study the response of QCD vacuum to strong magnetic fields, using a potential model for quark-antiquark interaction. find that production spin-polarized $u\ifmmode \bar{u}\else \={u}\fi{}$ pairs is energetically favorable fields $B&gt;{B}_{\mathrm{crit}}\ensuremath{\sim}10 {\mathrm{GeV}}^{2}.$ contrast resulting condensate with quark which present at zero field, and we estimate corresponding magnetization as function B.

We advocate a set of approximations for studying the finite temperature behavior strongly-coupled theories in 0+1 dimensions. The approximation consists expanding about Gaussian action, with width determined by gap equations. can be applied to supersymmetric systems, provided that equations are formulated superspace. It large-N theories, keeping just planar contribution analyze several models scalar quantum mechanics, and show correctly distinguishes between moduli space, mass gap,...

We investigate the late-time behavior of a universe containing supergravity gas and wrapped 2-branes in context M theory compactified on ${T}^{10}.$ The tends to drive uniform expansion, while branes impede expansion directions about which they are wrapped. Assuming spatial homogeneity, we study dynamics both numerically analytically. At late times radii obey power laws determined by brane wrapping numbers, leading interesting hierarchies scale between unwrapped dimensions. biggest hierarchy...

We develop an approximation scheme for the quantum mechanics of N D0-branes at finite temperature in 't Hooft large-N limit. The entropy calculated using this agrees well with Bekenstein-Hawking a ten-dimensional non-extremal black hole 0-brane charge. This result is accord duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. Our provides model density matrix which describes strongly-coupled mechanics.

We consider corrections to the entropy of a black hole from an $O(N)$ invariant linear $\s$-model. obtain $1/N$ expansion partition function on cone. The arises diagrams which are analogous those introduced by Susskind and Uglum explain in string theory. interpretation \sm depends scale. At short distances, it has state counting interpretation, as entanglement $N$ fields $\pa$. In infrared, effective theory single composite field $\s \sim \pa \pa$, is lost.

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

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

We present the details of a mean-field approximation scheme for quantum mechanics N D0-branes at finite temperature. The can be applied strong 't Hooft coupling. find that resulting entropy is in good agreement with Bekenstein-Hawking ten-dimensional nonextremal black hole 0-brane charge. This result accord duality conjectured by Itzhaki, Maldacena, Sonnenschein and Yankielowicz. study spectrum single-string excitations within mechanics, evidence clear separation between light heavy degrees...