arXiv subjects

Donald Marolf

Publications and source records attributed to Donald Marolf.

At least 145 records · Page 8Linked to original sources

arXiv2008

Group Averaging of massless scalar fields in 1+1 de Sitter

Perturbative gravity in global de Sitter space is subject to so-called linearization stability constraints: If they are to couple consistently to the gravitational field, quantum states must be invariant under the de Sitter isometries. While standard Fock spaces contain no de Sitter-invariant states apart from (possibly) the vacuum, a full Hilbert space of de Sitter-invariant quantum states can be constructed via group averaging techiniques. We re-examine the simple toy model of de Sitter group averaging given by the free 1+1 scalar field, expanding on an earlier analysis by Higuchi. Our purpose is twofold: to include the scalar zero-mode, and to explicitly count the number of de Sitter-invariant states as a function of an appropriately defined energy.

gr-qc↗

arXiv2008

On the Stress Tensor for Asymptotically Flat Gravity

The recent introduction of a boundary stress tensor for asymptotically flat spacetimes enabled a new construction of energy, momentum, and Lorentz charges. These charges are known to generate the asymptotic symmetries of the theory, but their explicit formulas are not identical to previous constructions in the literature. This paper corrects an earlier comparison with other approaches, including terms in the definition of the stress tensor charges that were previously overlooked. We show that these terms either vanish identically (for d > 4) or take a form that does not contribute to the conserved charges (for d=4). This verifies the earlier claim that boundary stress tensor methods for asymptotically flat spacetimes yield the same conserved charges as other approaches. We also derive some additional connections between the boundary stress tensor and the electric part of the Weyl tensor.

hep-th↗

arXiv2008

A tale of two superpotentials: Stability and Instability in Designer Gravity

We investigate the stability of asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound. The boundary conditions in these ``designer gravity'' theories are defined in terms of an arbitrary function W. Previous work had suggested that the energy in designer gravity is bounded below if i) W has a global minimum and ii) the scalar potential admits a superpotential P. More recently, however, certain solutions were found (numerically) to violate the proposed energy bound. We resolve the discrepancy by observing that a given scalar potential can admit two possible branches of the corresponding superpotential, P_{\pm}. When there is a P_- branch, we rigorously prove a lower bound on the energy; the P_+ branch alone is not sufficient. Our numerical investigations i) confirm this picture, ii) confirm other critical aspects of the (complicated) proofs, and iii) suggest that the existence of P_- may in fact be necessary (as well as sufficient) for the energy of a designer gravity theory to be bounded below.

hep-th↗

arXiv2007

Collisions with Black Holes and Deconfined Plasmas

We use AdS/CFT to investigate i) high energy collisions with balls of deconfined plasma surrounded by a confining phase and ii) the rapid localized heating of a deconfined plasma. Both of these processes are dual to collisions with black holes, where they result in the nucleation of a new "arm" of the horizon reaching out in the direction of the incident object. We study the resulting non-equilibrium dynamics in a universal limit of the gravitational physics which may indicate universal behavior of deconfined plasmas at large N_c. Process (i) produces "virtual" arms of the plasma ball, while process (ii) can nucleate surprisingly large bubbles of a higher temperature phase.

hep-th↗

arXiv2007

The Physical Process First Law for Bifurcate Killing Horizons

The physical process version of the first law for black holes states that the passage of energy and angular momentum through the horizon results in a change in area $\fracκ{8 π} ΔA = ΔE - ΩΔJ$, so long as this passage is quasi-stationary. A similar physical process first law can be derived for any bifurcate Killing horizon in any spacetime dimension $d \ge 3$ using much the same argument. However, to make this law non-trivial, one must show that sufficiently quasi-stationary processes do in fact occur. In particular, one must show that processes exist for which the shear and expansion remain small, and in which no new generators are added to the horizon. Thorne, MacDonald, and Price considered related issues when an object falls across a d=4 black hole horizon. By generalizing their argument to arbitrary $d \ge 3$ and to any bifurcate Killing horizon, we derive a condition under which these effects are controlled and the first law applies. In particular, by providing a non-trivial first law for Rindler horizons, our work completes the parallel between the mechanics of such horizons and those of black holes for $d \ge 3$. We also comment on the situation for d=2.

gr-qc↗

arXiv2007

A global picture of quantum de Sitter space

Perturbative gravity about a de Sitter background motivates a global picture of quantum dynamics in `eternal de Sitter space,' the theory of states which are asymptotically de Sitter to both future and past. Eternal de Sitter physics is described by a finite dimensional Hilbert space in which each state is precisely invariant under the full de Sitter group. This resolves a previously-noted tension between de Sitter symmetry and finite entropy. Observables, implications for Boltzmann brains, and Poincare recurrences are briefly discussed.

hep-th↗

arXiv2007

Holographic Renormalization of Gravity in Little String Theory Duals

We perform a holographic renormalization of gravity duals to little string theories. In particular, we construct counterterms which yield a well-defined type II action for NS-sector linear dilaton backgrounds. Our methods are based on a similar recent construction in asymptotically flat spacetimes, and our work demonstrates in detail the parallels between asymptotically flat and linear dilaton boundary conditions. The counterterms guarantee that (i) the on-shell action is finite and (ii) asymptotically linear dilaton solutions are stationary points of the action under all boundary condition preserving variations. We use the resulting action to compute a boundary stress tensor and the associated conserved charges.

hep-th↗

arXiv2007

Reversing Renormalization-Group Flows with AdS/CFT

For scalar fields in AdS with masses slightly above the Breitenlohner-Freedman bound, appropriate non-local boundary conditions can define a unitary theory. Such boundary conditions correspond to non-local deformations of the dual CFT, and generate a non-local renormalization-group flow. Nevertheless, a bulk analysis suggests that certain such flows lead to local CFTs in the infra-red. Since the flows are non-local, they can either increase or decrease the central charge of the CFT. In fact, given any local renormalization-group flow within a certain general class which leads from a UV theory (CFT_1) to an IR theory (CFT_2), we show that one can find such a non-local flow in which the endpoints are interchanged: the non-local theory flows from CFT_2 in the IR to CFT_1 in the UV. We work at large N, but the flows we consider involve quantum field effects in the bulk, corresponding to 1/N corrections in the dual theory.

hep-th↗

arXiv2007

Asymptotic Flatness, Little String Theory, and Holography

We argue that any non-gravitational holographic dual to asymptotically flat string theory in $d$-dimensions naturally resides at spacelike infinity. Since spacelike infinity can be resovled as a $(d-1)$-dimensional timelike hyperboloid (i.e., as a copy of de Sitter space in $(d-1)$ dimensions), the dual theory is defined on a Lorentz signature spacetime. Conceptual issues regarding such a duality are clarified by comparison with linear dilaton boundary conditions, such as those dual to little string theory. We compute both time-ordered and Wightman boundary 2-point functions of operators dual to massive scalar fields in the asymptotically flat bulk.

hep-th↗

arXiv2007

Energy Bounds in Designer Gravity

We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar fields with mass at or slightly above the Breitenlohner-Freedman bound in d greater than or equal to 4 spacetime dimensions. The boundary conditions in these ``designer gravity'' theories are defined in terms of an arbitrary function W. We give a general argument that the Hamiltonian generators of asymptotic symmetries for such systems will be finite, and proceed to construct these generators using the covariant phase space method. The direct calculation confirms that the generators are finite and shows that they take the form of the pure gravity result plus additional contributions from the scalar fields. By comparing the generators to the spinor charge, we derive a lower bound on the gravitational energy when i) W has a global minimum, ii) the Breitenlohner-Freedman bound is not saturated, and iii) the scalar potential V admits a certain type of "superpotential."

hep-th↗

arXiv2006

Asymptotic generators of fermionic charges and boundary conditions preserving supersymmetry

We use a covariant phase space formalism to give a general prescription for defining Hamiltonian generators of bosonic and fermionic symmetries in diffeomorphism invariant theories, such as supergravities. A simple and general criterion is derived for a choice of boundary condition to lead to conserved generators of the symmetries on the phase space. In particular, this provides a criterion for the preservation of supersymmetries. For bosonic symmetries corresponding to diffeomorphisms, our prescription coincides with the method of Wald et al. We then illustrate these methods in the case of certain supergravity theories in $d=4$. In minimal AdS supergravity, the boundary conditions such that the supercharges exist as Hamiltonian generators of supersymmetry transformations are unique within the usual framework in which the boundary metric is fixed. In extended ${\mathcal N}=4$ AdS supergravity, or more generally in the presence of chiral matter superfields, we find that there exist many boundary conditions preserving ${\mathcal N}=1$ supersymmetry for which corresponding generators exist. These choices are shown to correspond to a choice of certain arbitrary boundary ``superpotentials,'' for suitably defined ``boundary superfields.'' We also derive corresponding formulae for the conserved bosonic charges, such as energy, in those theories, and we argue that energy is always positive, for any supersymmetry-preserving boundary conditions. We finally comment on the relevance and interpretation of our results within the AdS-CFT correspondence.

gr-qc↗

arXiv2006

Observables in effective gravity

We address the construction and interpretation of diffeomorphism-invariant observables in a low-energy effective theory of quantum gravity. The observables we consider are constructed as integrals over the space of coordinates, in analogy to the construction of gauge-invariant observables in Yang-Mills theory via traces. As such, they are explicitly non-local. Nevertheless we describe how, in suitable quantum states and in a suitable limit, the familiar physics of local quantum field theory can be recovered from appropriate such observables, which we term `pseudo-local.' We consider measurement of pseudo-local observables, and describe how such measurements are limited by both quantum effects and gravitational interactions. These limitations support suggestions that theories of quantum gravity associated with finite regions of spacetime contain far fewer degrees of freedom than do local field theories.

hep-th↗

arXiv2006

Covariant Counterterms and Conserved Charges in Asymptotically Flat Spacetimes

Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved quantities at spatial infinity. Here we connect such results to other formalisms by showing explicitly i) that for spacetime dimension $d \ge 4$ the canonical form of the above-mentioned covariant action is precisely the ADM action, with the familiar ADM boundary terms and ii) that for $d=4$ the conserved quantities defined by counter-term methods agree precisely with the Ashtekar-Hansen conserved charges at spatial infinity.

gr-qc↗

arXiv2006

Boundary Conditions and Dualities: Vector Fields in AdS/CFT

In AdS, scalar fields with masses slightly above the Breitenlohner-Freedman bound admit a variety of possible boundary conditions which are reflected in the Lagrangian of the dual field theory. Generic small changes in the AdS boundary conditions correspond to deformations of the dual field theory by multi-trace operators. Here we extend this discussion to the case of vector gauge fields in the bulk spacetime using the results of Ishibashi and Wald [hep-th/0402184]. As in the context of scalar fields, general boundary conditions for vector fields involve multi-trace deformations which lead to renormalization-group flows. Such flows originate in ultra-violet CFTs which give new gauge/gravity dualities. At least for AdS4/CFT3, the dual of the bulk photon appears to be a propagating gauge field instead of the usual R-charge current. Applying similar reasoning to tensor fields suggests the existence of a duality between string theory on AdS4 and a quantum gravity theory in three dimensions.

hep-th↗

arXiv2006

States and Boundary Terms: Subtleties of Lorentzian AdS/CFT

We complete the project of specifying the Lorentzian AdS/CFT correspondence and its approximation by bulk semi-classical methods begun by earlier authors. At the end, the Lorentzian treatment is self-contained and requires no analytic continuation from the Euclidean. The new features involve a careful study of boundary terms associated with an initial time $t_-$ and a final time $t_+$. These boundary terms are determined by a choice of quantum states. The main results in the semi-classical approximation are 1) The times $t_\pm$ may be finite, and need only label Cauchy surfaces respectively to the past and future of the points at which one wishes to obtain CFT correlators. Subject to this condition on $t_\pm$, we provide a bulk computation of CFT correlators that is manifestly independent of $t_\pm$. 2) As a result of (1), all CFT correlators can be expressed in terms of a path integral over regions of spacetime {\it outside} of any black hole horizons. 3) The details of the boundary terms at $t_\pm$ serve to guarrantee that, at leading order in this approximation, any CFT one-point function is given by a simple boundary value of the classical bulk solution at null infinity, $I$. This work is dedicated to the memory of Bryce S. DeWitt. The remarks in this paper largely study the relation of the AdS/CFT dictionary to the Schwinger variational principle, which the author first learned from DeWitt as a Ph.D. student.

hep-th↗

arXiv2006

Information Recovery From Black Holes

We argue that if black hole entropy arises from a finite number of underlying quantum states, then any particular such state can be identified from infinity. The finite density of states implies a discrete energy spectrum, and, in general, such spectra are non-degenerate except as determined by symmetries. Therefore, knowledge of the precise energy, and of other commuting conserved charges, determines the quantum state. In a gravitating theory, all conserved charges including the energy are given by boundary terms that can be measured at infinity. Thus, within any theory of quantum gravity, no information can be lost in black holes with a finite number of states. However, identifying the state of a black hole from infinity requires measurements with Planck scale precision. Hence observers with insufficient resolution will experience information loss.

hep-th↗

arXiv2006

The non-zero energy of 2+1 Minkowski space

We compute the energy of 2+1 Minkowski space from a covariant action principle. Using Ashtekar and Varadarajan's characterization of 2+1 asymptotic flatness, we first show that the 2+1 Einstein-Hilbert action with Gibbons-Hawking boundary term is both finite on-shell (apart from past and future boundary terms) and stationary about solutions under arbitrary smooth asymptotically flat variations of the metric. Thus, this action provides a valid variational principle and no further boundary terms are required. We then obtain the gravitational Hamiltonian by direct computation from this action. The result agrees with the Hamiltonian of Ashtekar and Varadarajan up to an overall addititve constant. This constant is such that 2+1 Minkowski space is assigned the energy E = -1/4G, while the upper bound on the energy is set to zero. Any variational principle with a boundary term built only from the extrinsic and intrinsic curvatures of the boundary is shown to lead to the same result. Interestingly, our result is not the flat-space limit of the corresponding energy -1/8G of 2+1 anti-de Sitter space.

hep-th↗

arXiv2006

Holographic Renormalization of Asymptotically Flat Spacetimes

A new local, covariant ``counter-term'' is used to construct a variational principle for asymptotically flat spacetimes in any spacetime dimension $ d \ge 4$. The new counter-term makes direct contact with more familiar background subtraction procedures, but is a local algebraic function of the boundary metric and Ricci curvature. The corresponding action satisfies two important properties required for a proper treatment of semi-classical issues and, in particular, to connect with any dual non-gravitational description of asymptotically flat space. These properties are that 1) the action is finite on-shell and 2) asymptotically flat solutions are stationary points under {\it all} variations preserving asymptotic flatness; i.e., not just under variations of compact support. Our definition of asymptotic flatness is sufficiently general to allow the magentic part of the Weyl tensor to be of the same order as the electric part and thus, for d=4, to have non-vanishing NUT charge. Definitive results are demonstrated when the boundary is either a cylindrical or a hyperbolic (i.e., de Sitter space) representation of spacelike infinity ($i^0$), and partial results are provided for more general representations of $i^0$. For the cylindrical or hyperbolic representations of $i^0$, similar results are also shown to hold for both a counter-term proportional to the square-root of the boundary Ricci scalar and for a more complicated counter-term suggested previously by Kraus, Larsen, and Siebelink. Finally, we show that such actions lead, via a straightforward computation, to conserved quantities at spacelike infinity which agree with, but are more general than, the usual (e.g., ADM) results.

hep-th↗