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Erik Verlinde

Publications and source records attributed to Erik Verlinde.

52 records · Page 3Linked to original sources
arXiv2002

Elliptic de Sitter Space: dS/Z_2

We propose that for every event in de Sitter space, there is a CPT-conjugate event at its antipode. Such an ``elliptic'' $Z_2$-identification of de Sitter space provides a concrete realization of observer complementarity: every observer has complete information. It is possible to define the analog of an S-matrix for quantum gravity in elliptic de Sitter space that is measurable by all observers. In a holographic description, S-matrix elements may be represented by correlation functions of a dual (conformal field) theory that lives on the single boundary sphere. S-matrix elements are de Sitter-invariant, but have different interpretations for different observers. We argue that Hilbert states do not necessarily form representations of the full de Sitter group, but just of the subgroup of rotations. As a result, the Hilbert space can be finite-dimensional and still have positive norm. We also discuss the elliptic interpretation of de Sitter space in the context of type IIB* string theory.

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arXiv2002

Penrose Limits and Non-local theories

We investigate Penrose limits of two classes of non-local theories, little string theories and non-commutative gauge theories. Penrose limits of the near-horizon geometry of NS5-branes help to shed some light on the high energy spectrum of little string theories. We attempt to understand renormalization group flow in these theories by considering Penrose limits wherein the null geodesic also has a radial component. In particular, we demonstrate that it is possible to construct a pp-wave spacetime which interpolates between the linear dilaton and the AdS regions for the Type IIA NS5-brane. Similar analysis is considered for the holographic dual geometry to non-commutative field theories.

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arXiv2002

Strings from Quivers, Membranes from Moose

We consider N=2 moose/quiver gauge theories corresponding to N_1 D3-branes at a C^2/Z_{N_2} singularity in the ``large moose'' limit where N_1 and N_2 are scaled to infinity together. In the dual holographic description, this scaling gives rise to a maximally supersymmetric pp-wave background with a compact light-cone direction. We identify the gauge theory operators that describe the Discrete Light-Cone Quantization (DLCQ) of the string in this background. For each discrete light-cone momentum and winding sector there is a separate ground state and Fock space. The large moose/quiver diagram provides a useful graphical representation of the string and its excitations. This representation has a natural explanation in a T-dual language. The dual theory is a non-relativistic type IIA string wound around the T-dual direction, and bound by a quadratic Newtonian potential. We end with some comments on D-string/D-particle states, a possible lift to M-theory and the relation to deconstruction.

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arXiv2001

CFT and Entropy on the Brane

We consider a brane-universe in the background of an Anti-de Sitter/ Schwarschild geometry. We show that the induced geometry of the brane is exactly given by that of a standard radiation dominated FRW-universe. The radiation is represented by a strongly coupled CFT with an AdS-dual description. We show that when the brane crosses the horizon of the AdS-black hole the entropy and temperature are simply expressed in the Hubble constant and its time derivative. We present formulas for the entropy of the CFT which are generally valid, and which at the horizon coincide with the FRW equations. These results shed new light on recently proposed entropy bounds in the context of cosmology.

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arXiv2000

On the Holographic Principle in a Radiation Dominated Universe

The holographic principle is studied in the context of a $n+1$ dimensional radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The radiation is represented by a conformal field theory with a large central charge. Following recent ideas on holography, it is argued that the entropy density in the early universe is bounded by a multiple of the Hubble constant. The entropy of the CFT is expressed in terms of the energy and the Casimir energy via a universal Cardy formula that is valid for all dimensions. A new purely holographic bound is postulated which restricts the sub-extensive entropy associated with the Casimir energy. Unlike the Hubble bound, the new bound remains valid throughout the cosmological evolution. When the new bound is saturated the Friedman equation exactly coincides with the universal Cardy formula, and the temperature is uniquely fixed in terms of the Hubble parameter and its time-derivative.

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arXiv1999

On RG-flow and the Cosmological Constant

The AdS/CFT correspondence implies that the effective action of certain strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation of 5d gravity. Using an analogy with the relativistic point particle, I construct a low energy effective action that includes the Einstein action and obeys a Callan-Symanzik-type RG-flow equation. It follows from the flow equation that under quite general conditions the Einstein equations admit a flat space-time solution, but other solutions with non-zero cosmological constant are also allowed. I discuss the geometric interpretation of this result in the context of warped compactifications.

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arXiv1995

Global Aspects of Electric-Magnetic Duality

We show that the partition function of free Maxwell theory on a generic Euclidean four-manifold transforms in a non-trivial way under electric-magnetic duality. The classical part of the partition sum can be mapped onto the genus-one partition function of a 2d toroidal model, without the oscillator contributions. This map relates electric-magnetic duality to modular invariance of the toroidal model and, conversely, the $O(d,d',\Z)$ duality to the invariance of Maxwell theory under the 4d mapping class group. These dualities and the relation between toroidal models and Maxwell theory can be understood by regarding both theories as dimensional reductions of a self-dual 2-form theory in six dimensions. Generalizations to more $U(1)$-gauge fields and reductions from higher dimensions are also discussed. We find indications that the Abelian gauge theories related to 4d string theories with $N=4$ space-time supersymmetry are exactly duality invariant.

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arXiv1995

Black Hole Horizons and Complementarity

We investigate the effect of gravitational back-reaction on the black hole evaporation process. The standard derivation of Hawking radiation is re-examined and extended by including gravitational interactions between the infalling matter and the outgoing radiation. We find that these interactions lead to substantial effects. In particular, as seen by an outside observer, they lead to a fast growing uncertainty in the position of the infalling matter as it approaches the horizon. We argue that this result supports the idea of black hole complementarity, which states that, in the description of the black hole system appropriate to outside observers, the region behind the horizon does not establish itself as a classical region of space-time. We also give a new formulation of this complementarity principle, which does not make any specific reference to the location of the black hole horizon.

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arXiv1995

Black Hole Evaporation and Complementarity

About twenty years ago Hawking made the remarkable suggestion that the black hole evaporation process will inevitably lead to a fundamental loss of quantum coherence. The mechanism by which the quantum radiation is emitted appears to be insensitive to the detailed history of the black hole, and thus it seems that most of the initial information is lost for an outside observer. However, direct examination of Hawking's original derivation (or any later one) of the black hole emission spectrum shows that one inevitably needs to make reference to particle waves that have arbitrarily high frequency near the horizon as measured in the reference frame of the in-falling matter. This exponential red-shift effect associated with the black hole horizon leads to a breakdown of the usual separation of length scales, and effectively works as a magnifying glass that makes the consequences of the short distance, or rather, high energy physics near the horizon visible at larger scales to an asymptotic observer.

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arXiv1993

QCD at High Energies and Two-Dimensional Field Theory

Previous studies of high-energy scattering in QCD have shown a remarkable correspondence with two-dimensional field theory. In this paper we formulate a simple effective model in which this two-dimensional nature of the interactions is manifest. Starting from the (3+1)-dimensional Yang-Mills action, we implement the high energy limit $s\! >\! > \! t$ via a scaling argument and we derive from this a simplified effective theory. This effective theory is still (3+1)-dimensional, but we show that its interactions can to leading order be summarized in terms of a two-dimensional sigma-model defined on the transverse plane. Finally, we verify that our formulation is consistent with known perturbative results. This is a revised and extended version of hep-th 9302104. In particular, we have added a section that clarifies the connection with Lipatov's gluon emission vertex.

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arXiv1993

Quantum Black Hole Evaporation

We investigate a recently proposed model for a full quantum description of two-dimensional black hole evaporation, in which a reflecting boundary condition is imposed in the strong coupling region. It is shown that in this model each initial state is mapped to a well-defined asymptotic out-state, provided one performs a certain projection in the gravitational zero mode sector. We find that for an incoming localized energy pulse, the corresponding out-going state contains approximately thermal radiation, in accordance with semi-classical predictions. In addition, our model allows for certain acausal strong coupling effects near the singularity, that give rise to corrections to the Hawking spectrum and restore the coherence of the out-state. To an asymptotic observer these corrections appear to originate from behind the receding apparent horizon and start to influence the out-going state long before the black hole has emitted most of its mass. Finally, by putting the system in a finite box, we are able to derive some algebraic properties of the scattering matrix and prove that the final state contains all initial information.

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arXiv1993

A Unitary S-matrix for 2D Black Hole Formation and Evaporation

We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled to $N$ massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and derive the quantum quantum $S$-matrix for the case that $N$=$24$. This $S$-matrix is unitary by construction, and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity $S$-matrix and that of the $c=1$ matrix model.

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arXiv1992

The Master Equation of 2D String Theory

A general method is presented for deriving on-shell Ward-identities in (2D) string theory. It is shown that all tree-level Ward identities can be summarized in a quadratic differential equation for the generating function of tree-amplitudes. This result is extended to loop amplitudes and leads to a master equation {\it à la} Batalin-Vilkovisky for the complete partition function.

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arXiv1991

Duality, Quotients, and Currents

We study the generalization of $R\to 1/R$ duality to arbitrary conformally invariant sigma models with an isometry. We show that any pair of dual sigma models can be represented as quotients of a self-dual sigma model obtained by gauging different combinations of chiral currents. This observation is used to clarify the interpretation of the generalized duality as a symmetry of conformal field theory. We extend these results to $N=2$ supersymmetric sigma models.

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arXiv1991

Scattering at Planckian Energies

We give a systematic analysis of forward scattering in 3$+$1-dimensional quantum gravity, at center of mass energies comparable or larger than the Planck energy. We show that quantum gravitational effects in this kinematical regime are described by means of a topological field theory. We find that the scattering amplitudes display a universal behaviour very similar to two dimensional string amplitudes, thereby recovering results obtained previously by 't Hooft. Finally, we discuss the two-particle process in some detail.

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