# Amsel, Marolf, Virmani ## The physical process first law for bifurcate Killing horizons \[Links: [arXiv](https://arxiv.org/abs/0708.2738), [PDF](https://arxiv.org/pdf/0708.2738.pdf)\] \[Abstract: \] ## Summary - horizon dynamics are quite general except [[0409 Physical process version of the first law]], where issues were raised in [[JacobsonParentani2003]]; this paper clarifies these issues - show that ==quasi-stationary== processes do exist for BHs with ==bifurcate horizons== ## Issues - caustics - [[0229 Membrane paradigm]] says that the absorption of an object of mass $m$ and radius $r$ by a black hole of mass $M$ will result in caustics when $r\ll \sqrt{mM}$. Since Rindler horizon can be thought of $M\to \infty$ limit of a BH, caustics would always form! - problems: expansion becomes large; caustics usually signal new generators to the horizon ## Quasi-stationary - requires that 1) the expansion and shear along each generator remain weak enough to neglect 2nd order terms and 2) no new generators are added to the horizon ## Caustics - [[ThornePriceMacDonald1986Book]] showed (using [[0229 Membrane paradigm]]) that caustics form if $r\ll \sqrt{mM}$, but the paper provides a more local criterium: $r \sim \sqrt{E_{\chi} / \kappa}$ (more generally $r^{d-2} \sim E_{\chi} / \kappa$) # Benincasa, Cachazo ## Consistency Conditions on the S-Matrix of Massless Particles \[Links: [arXiv](https://arxiv.org/abs/0705.4305), [PDF](https://arxiv.org/pdf/0705.4305.pdf)\] \[Abstract: We introduce a set of consistency conditions on the S-matrix of theories of massless particles of arbitrary spin in four-dimensional Minkowski space-time. We find that in most cases the constraints, derived from the conditions, can only be satisfied if the S-matrix is trivial. Our conditions apply to theories where four-particle scattering amplitudes can be obtained from three-particle ones via a recent technique called [[0058 BCFW|BCFW]] construction. We call theories in this class [[0551 On-shell recursion relations|constructible]]. We propose a program for performing a systematic search of constructible theories that can have non-trivial S-matrices. As illustrations, we provide simple proofs of already known facts like the impossibility of spin $s > 2$ non-trivial S-matrices, the impossibility of several spin 2 interacting particles and the uniqueness of a theory with spin 2 and spin 3/2 particles.\] # Bhattacharyya, Hubeny, Minwalla, Rangamani ## Nonlinear Fluid Dynamics from Gravity \[Links: [arXiv](https://arxiv.org/abs/0712.2456), [PDF](https://arxiv.org/pdf/0712.2456.pdf)\] \[Abstract: Black branes in AdS5 appear in a four parameter family labeled by their velocity and temperature. Promoting these parameters to Goldstone modes or collective coordinate fields -- arbitrary functions of the coordinates on the boundary of AdS5 -- we use Einstein's equations together with regularity requirements and boundary conditions to determine their dynamics. The resultant equations turn out to be those of boundary fluid dynamics, with specific values for fluid parameters. Our analysis is perturbative in the boundary derivative expansion but is valid for arbitrary amplitudes. Our work may be regarded as a derivation of the nonlinear equations of boundary fluid dynamics from gravity. As a concrete application we find an explicit expression for the expansion of this fluid stress tensor including terms up to second order in the derivative expansion.\] ## Summary - OG for [[0228 Fluid-gravity correspondence|fluid-gravity correspondence]] # Boels, Mason, Skinner ## From Twistor Actions to MHV Diagrams \[Links: [arXiv](https://arxiv.org/abs/hep-th/0702035), [PDF](https://arxiv.org/pdf/hep-th/0702035.pdf)\] \[Abstract: We show that [[0061 Maximally helicity violating amplitudes|MHV]] diagrams are the Feynman diagrams of certain [[0330 Twistor theory|twistor]] actions for gauge theories in an axial gauge. The gauge symmetry of the twistor action is larger than that on space-time and this allows us to fix a gauge that makes the MHV formalism manifest but which is inaccessible from space-time. The framework is extended to describe matter fields: as an illustration we explicitly construct twistor actions for an adjoint scalar with arbitrary polynomial potential and a fermion in the fundamental representation and show how this leads to additional towers of MHV vertices in the MHV diagram formalism.\] # Brigante, Liu, Myers, Shenker, Yaida ## Viscosity Bound Violation in Higher Derivative Gravity \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to [[0554 Einstein gravity|Einstein gravity]] with curvature square [[0006 Higher-derivative gravity|corrections]]. After field redefinitions these theories reduce to [[0425 Gauss-Bonnet gravity|Gauss-Bonnet gravity]], which has special properties that allow us to compute the [[0430 Holographic shear viscosity|shear viscosity]] nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.\] # Calabrese, Cardy (Apr) ## Quantum Quenches in Extended Systems \[Links: [arXiv](https://arxiv.org/abs/0704.1880), [PDF](https://arxiv.org/pdf/0704.1880.pdf)\] \[Abstract: We study in general the time-evolution of correlation functions in a extended quantum system after the [[0558 Quantum quench|quench]] of a parameter in the hamiltonian. We show that correlation functions in $d$ dimensions can be extracted using methods of boundary critical phenomena in $d+1$ dimensions. For $d=1$ this allows to use the powerful tools of [[0481 Conformal field theory|conformal field theory]] in the case of critical evolution. Several results are obtained in generic dimension in the gaussian (mean-field) approximation. These predictions are checked against the real-time evolution of some solvable models that allows also to understand which features are valid beyond the critical evolution. All our findings may be explained in terms of a picture generally valid, whereby [[0518 Quasiparticle model|quasiparticles]], entangled over regions of the order of the correlation length in the initial state, then propagate with a finite speed through the system. Furthermore we show that the long-time results can be interpreted in terms of a generalized Gibbs ensemble. We discuss some open questions and possible future developments.\] # Cornalba ## Eikonal Methods in AdS/CFT: Regge Theory and Multi-Reggeon Exchange \[Links: [arXiv](https://arxiv.org/abs/0710.5480), [PDF](https://arxiv.org/pdf/0710.5480.pdf)\] \[Abstract: We analyze conformal field theory 4-point functions of the form $A ~ O_1(x_1) O_2(x_2) O_1(x_3) O_2(x_4)$, where the operators $O_i$ are scalar primaries. We show that, in the Lorentzian regime, the limit $x_1 \to x_3$ is dominated by the exchange of conformal partial waves of highest spin. When partial waves of arbitrary spin contribute to $A$, the behavior of the Lorentzian amplitude for $x_1 \to x_3$ must be analyzed using complex-spin techniques, leading to a generalized Regge theory for CFT's. Whenever the CFT is dual to a string theory, the string tree-level contribution $A_\text{tree}$ to the amplitude $A$ presents a Regge pole corresponding the a gravi-reggeon exchange. In this case, we apply the impact parameter representation for CFT amplitudes, previously developed, to analyze multiple reggeon exchanges in the eikonal limit. As an example, we apply these general techniques to $\mathcal{N}=4$ super-Yang-Mills theory in $d=4$ in the limit of large 't Hooft coupling, including the leading string corrections to pure graviton exchange.\] # Cornalba, Costa, Penedones ## Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion \[Links: [arXiv](https://arxiv.org/abs/0707.0120), [PDF](https://arxiv.org/pdf/0707.0120.pdf)\] \[Abstract: We derive an eikonal approximation to high energy interactions in Anti-de Sitter spacetime, by generalizing a position space derivation of the eikonal amplitude in flat space. We are able to resum, in terms of a generalized phase shift, ladder and cross ladder graphs associated to the exchange of a spin $j$ field, to all orders in the coupling constant. Using the [[0001 AdS-CFT|AdS/CFT correspondence]], the resulting amplitude determines the behavior of the dual conformal field theory four point function $\langle O_1 O_2 O_1 O_2 \rangle$ for small values of the cross ratios, in a Lorentzian regime. Finally we show that the phase shift is dominated by graviton exchange and computes, in the dual CFT, the anomalous dimension of the double trace primary operators $O_1 \partial ... \partial O_2$ of large dimension and spin, corresponding to the relative motion of the two interacting particles. The results are valid at strong t'Hooft coupling and are exact in the $1/N$ expansion.\] # Dohse (Thesis) ## Configuration space methods and time ordering for scalar propagators in (A)dS \[Links: [arXiv](https://arxiv.org/abs/0706.1887), [PDF](https://arxiv.org/pdf/0706.1887.pdf)\] \[Abstract: \] ## Remarks - Master's thesis summarising different [[0125 Scalar field propagator in AdS]] # Eynard, Orantin ## Invariants of algebraic curves and topological expansion \[Links: [arXiv](https://arxiv.org/abs/), [PDF](https://arxiv.org/pdf/.pdf)\] \[Abstract: For any arbitrary algebraic curve, we define an infinite sequence of invariants. We study their properties, in particular their variation under a variation of the curve, and their modular properties. We also study their limits when the curve becomes singular. In addition we find that they can be used to define a formal series, which satisfies formally an Hirota equation, and we thus obtain a new way of constructing a tau function attached to an algebraic curve. These invariants are constructed in order to coincide with the topological expansion of a [[0197 Matrix model|matrix formal integral]], when the algebraic curve is chosen as the large $N$ limit of the matrix model's spectral curve. Surprisingly, we find that the same invariants also give the topological expansion of other models, in particular the matrix model with an external field, and the so-called double scaling limit of matrix models, i.e. the $(p,q)$ minimal models of conformal field theory. As an example to illustrate the efficiency of our method, we apply it to the Kontsevitch integral, and we give a new and extremely easy proof that Kontsevitch integral depends only on odd times, and that it is a KdV $\tau$-function.\] # Gaiotto, Yin ## Notes on Superconformal Chern-Simons-Matter Theories \[Links: [arXiv](https://arxiv.org/abs/0704.3740), [PDF](https://arxiv.org/pdf/0704.3740)\] \[Abstract: The three dimensional $\mathscr{N}=2$ supersymmetric [[0089 Chern-Simons theory|Chern-Simons theory]] coupled to matter fields, possibly deformed by a superpotential, give rise to a large class of exactly conformal theories with Lagrangian descriptions. These theories can be arbitrarily weakly coupled, and hence can be studied perturbatively. We study the theories in the large $N$ limit, and compute the two-loop anomalous dimension of certain long operators. Our result suggests that various $\mathscr{N}=2$ $U(N)$ Chern-Simons theories coupled to suitable matter fields are dual to open or closed string theories in AdS4, which are not yet constructed.\] # Gourgoulhon (Lectures) ## 3+1 Formalism and Bases of Numerical Relativity \[Links: [arXiv](https://arxiv.org/abs/gr-qc/0703035), [PDF](https://arxiv.org/pdf/gr-qc/0703035.pdf)\] \[Abstract: \] # Graham, Olum ## Achronal averaged null energy condition \[Links: [arXiv](https://arxiv.org/abs/0705.3193), [PDF](https://arxiv.org/pdf/0705.3193.pdf)\] \[Abstract: The [[0417 Averaged null energy condition|averaged null energy condition]] (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This condition is sufficient to prove many important theorems in general relativity, but it is violated by quantum fields in curved spacetime. However there is a weaker condition, which is free of known violations, requiring only that there is no self-consistent space-time in semiclassical gravity in which ANEC is violated on a complete, *achronal* null geodesic. We indicate why such a condition might be expected to hold and show that it is sufficient to rule out [[0083 Traversable wormhole|wormholes]] and closed timelike curves.\] # Hayden, Preskill ## Black holes as mirrors: quantum information in random subsystems \[Links: [arXiv](https://arxiv.org/abs/0708.4025), [PDF](https://arxiv.org/pdf/0708.4025.pdf)\] \[Abstract: We study [[0131 Information paradox|information retrieval from evaporating black holes]], assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted [[0304 Hawking radiation|Hawking radiation]]. If the evaporation of the black hole has already proceeded past the "half-way" point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for [[0146 Quantum error correction|quantum error-correcting codes]] that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the [[0347 Black hole complementarity|black hole complementarity]] hypothesis.\] ## Refs - [[0217 Hayden-Preskill decoding criterion]] ## Classical randomiser - to see why this is somehow classical: we are not permuting the $n$ bits Alice throws in, but we are permuting the state: there are $(2n)!$ ways of permuting the string with $2^n$ possibles states to another state (i.e. it is a map from state to state) ## Thermalisation time - the argument assumes that the BH thermalises in a time scale comparable to the interval between particle emissions $\sim r_S$ - a [[0229 Membrane paradigm|membrane picture]] helps establish this # Hubeny, Rangamani, Takayanagi ## A covariant holographic entanglement entropy proposal \[Links: [arXiv](https://arxiv.org/abs/0705.0016), [PDF](https://arxiv.org/pdf/0705.0016.pdf)\] \[Abstract: \] ## Refs - this is the famous HRT paper - proof by [[2016#Dong, Lewkowycz, Rangamani]] - extension of [[2006#Ryu, Takayanagi (Mar)]] - [[0007 RT surface]] ## Proposal - area of a co-dim 2 surface with vanishing expansions of null *geodesics* ## Notion of time - in generic time-dependent background: no canonical time foliation - QFT on fixed background: there is natural notion of time - a the boundary foliation extends to the bulk in a *unique* way, then we can just find minimal surfaces on these spacelike surfaces # Maeda, Nozawa ## Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity \[Links: [arXiv](https://arxiv.org/abs/0709.1199), [PDF](https://arxiv.org/pdf/0709.1199.pdf)\] \[Abstract: We investigate properties of a quasi-local mass in a higher-dimensional spacetime having symmetries corresponding to the isomertries of an ($n-2$)-dimensional maximally symmetric space in [[0425 Gauss-Bonnet gravity|Einstein-Gauss-Bonnet gravity]] in the presence of a cosmological constant. We assume that the Gauss-Bonnet coupling constant is non-negative. The quasi-local mass was recently defined by one of the authors as a counterpart of the [[0595 Quasi-local energy#Misner-Sharp energy|Misner-Sharp quasi-local mass]] in general relativity. The quasi-local mass is found to be a quasi-local conserved charge associated with a locally conserved current constructed from the generalized Kodama vector and exhibits the unified first law corresponding to the energy-balance law. In the asymptotically flat case, it converges to the [[0487 ADM mass|Arnowitt-Deser-Misner mass]] at spacelike infinity, while it does to the Deser-Tekin and Padilla mass at infinity in the case of asymptotically AdS. Under the dominant energy condition, we show the monotonicity of the quasi-local mass for any $k$, while the positivity on an untrapped hypersurface with a regular center is shown for $k=1$ and for $k=0$ with an additional condition, where $k=\pm1,0$ is the constant sectional curvature of each spatial section of equipotential surfaces. Under a special relation between coupling constants, positivity of the quasi-local mass is shown for any $k$ without assumptions above. We also classify all the vacuum solutions by utilizing the generalized Kodama vector. Lastly, several conjectures on further generalization of the quasi-local mass in [[0341 Lovelock gravity|Lovelock gravity]] are proposed.\] ## Refs - Misner-Sharp for GB gravity was proposed earlier in [[2006#Maeda]] ## Notations - $\tilde{\alpha}:=(n-3)(n-4) \alpha$ - $\tilde{\Lambda}:=2 \Lambda /[(n-1)(n-2)]$ # Maloney, Witten ## QG partition function in 3d \[Links: [arXiv](https://arxiv.org/abs/0712.0155), [PDF](https://arxiv.org/pdf/0712.0155.pdf)\] \[Abstract: We consider pure [[0002 3D gravity|three-dimensional quantum gravity]] with a negative cosmological constant. The sum of known contributions to the partition function from classical geometries can be computed exactly, including quantum corrections. However, the result is not physically sensible, and if the model does exist, there are some additional contributions. One possibility is that the theory may have long strings and a continuous spectrum. Another possibility is that complex geometries need to be included, possibly leading to a holomorphically factorized partition function. We analyze the subleading corrections to the [[0004 Black hole entropy|Bekenstein-Hawking entropy]] and show that these can be correctly reproduced in such a holomorphically factorized theory. We also consider the [[0012 Hawking-Page transition|Hawking-Page phase transition]] between a thermal gas and a black hole and show that it is a phase transition of Lee-Yang type, associated with a condensation of zeros in the complex temperature plane. Finally, we analyze pure three-dimensional supergravity, with similar results.\] ## Refs - fixing of this problem by including different topologies [[2020#Maxfield, Turiaci]] - Maloney's fix by including conical geometries [[2020#Benjamin, Collier, Maloney]] # Olmo ## Limit to GR of f(R) \[Links: [arXiv](https://arxiv.org/abs/gr-qc/0612047), [PDF](https://arxiv.org/pdf/gr-qc/0612047.pdf)\] \[Abstract: \] ## Summary - reasons to introduce [[0140 Scalar-tensor theory]] representation - study the limit of Einstein - find that scalar-tensor rep. is well behaved even in this limit ## f(R) original form - action $S=\frac{1}{2 \kappa^{2}} \int d^{4} x \sqrt{-g} f(R)+S_{m}\left[g_{\mu \nu}, \psi_{m}\right]$ ## Scalar tensor form - action $S=\frac{1}{2 \kappa^{2}} \int d^{4} x \sqrt{-g}[\phi R-V(\phi)]+S_{m}\left[g_{\mu \nu}, \psi_{m}\right]$ - $\phi \equiv f^{\prime}(R)$ defined this way because this is the actual dynamic entity - $V(\phi) \equiv R(\phi) f^{\prime}-f(R(\phi))$ - condition - $f'(R)$ must be invertible - other conditions like $f''(R)\ne0$ is superfluous # Rigol, Dunjko, Olshanii ## Thermalization and its mechanism for generic isolated quantum systems \[Links: [arXiv](https://arxiv.org/abs/0708.1324), [PDF](https://arxiv.org/pdf/0708.1324.pdf)\] \[Abstract: Time dynamics of isolated many-body quantum systems has long been an elusive subject. Very recently, however, meaningful experimental studies of the problem have finally become possible, stimulating theoretical interest as well. Progress in this field is perhaps most urgently needed in the foundations of quantum statistical mechanics. This is so because in generic isolated systems, one expects nonequilibrium dynamics on its own to result in thermalization: a relaxation to states where the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable through the time-tested recipe of statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible, in a sense analogous to that in which dynamical chaos makes classical thermalization possible. For example, dynamical [[0008 Quantum chaos|chaos]] itself cannot occur in an isolated quantum system, where time evolution is linear and the spectrum is discrete. Underscoring that new rules could apply in this case, some recent studies even suggested that statistical mechanics may give wrong predictions for the outcomes of relaxation in such systems. Here we demonstrate that an isolated generic quantum many-body system does in fact relax to a state well-described by the standard statistical mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation and that thermalization happens instead at the level of individual eigenstates, as first proposed by J.M. Deutsch and M. Srednicki. A striking consequence of this eigenstate thermalization scenario is that the knowledge of a single many-body eigenstate suffices to compute thermal averages-any eigenstate in the microcanonical energy window will do, as they all give the same result.\] # Son, Starinets (Review) ## Viscosity, Black Holes, and Quantum Field Theory \[Links: [arXiv](https://arxiv.org/abs/0704.0240), [PDF](https://arxiv.org/pdf/0704.0240.pdf)\] \[Abstract: \] # Yin ## On Non-handlebody Instantons in 3D Gravity \[Links: [arXiv](https://arxiv.org/abs/0711.2803), [PDF](https://arxiv.org/pdf/0711.2803.pdf)\] \[Abstract: In this note we describe the contribution from non-handlebody geometries to the partition function of [[0002 3D gravity|three-dimensional pure gravity]] with negative cosmological constant on a Riemann surface of genus greater than one, extending previous considerations for handlebodies.\] # Witten (Jun) ## Three-dimensional gravity revisited \[Links: [arXiv](https://arxiv.org/abs/0706.3359), [PDF](https://arxiv.org/pdf/0706.3359.pdf)\] \[Abstract: We consider the problem of identifying the CFT's that may be dual to pure gravity in [[0002 3D gravity|three dimensions]] with negative cosmological constant. The c-theorem indicates that three-dimensional pure gravity is consistent only at certain values of the coupling constant, and the relation to [[0089 Chern-Simons theory|Chern-Simons]] gauge theory hints that these may be the values at which the dual CFT can be holomorphically factorized. If so, and one takes at face value the minimum mass of a [[0086 Banados-Teitelboim-Zanelli black hole|BTZ]] black hole, then the energy spectrum of three-dimensional gravity with negative cosmological constant can be determined exactly. At the most negative possible value of the cosmological constant, the dual CFT is very likely the monster theory of Frenkel, Lepowsky, and Meurman. The monster theory may be the first in a discrete series of CFT's that are dual to three-dimensional gravity. The partition function of the second theory in the sequence can be determined on a hyperelliptic Riemann surface of any genus. We also make a similar analysis of supergravity.\] ## Refs - [[0073 AdS3-CFT2]] ## Quantisation - seemingly unrenormalisable by power counting <- G has dimension of length - -> perhaps the quantum theory does not exist - not true because the classical theory is trivial - $R_{abcd}$ can be expressed in terms of $R_{ab}$ - Einstein equation -> $R_{ab}$ in terms of $g_{ab}$ - -> any counter term proportional to $\int d^3x \sqrt{g}$ on shell - -> renormalisation of cosmological constant - now any counter term that vanishes on shell can be removed by local metric redefinition - i.e. renormalisation of cosmo const + metric redef remove any divergence in perturbation theory