arXiv subjects

Mark Van Raamsdonk

Publications and source records attributed to Mark Van Raamsdonk.

At least 73 records · Page 4Linked to original sources

arXiv2012

Rindler Quantum Gravity

In this note, we explain how asymptotically globally AdS spacetimes can be given an alternate dual description as entangled states of a pair of hyperbolic space CFTs, which are associated with complementary Rindler wedges of the AdS geometry. The reduced density matrix encoding the state of the degrees of freedom in one of these CFTs describes the physics in a single wedge, which we can think of as the region of spacetime accessible to an accelerated observer in AdS. For pure AdS, this density matrix is thermal, and we argue that the microstates in this thermal ensemble correspond to spacetimes that are almost indistinguishable from a Rindler wedge of pure AdS away from the horizon, but with the horizon replaced by some kind of singularity where the geometrical description breaks down. This alternate description of AdS, based on patches associated with particular observers, may give insight into the holographic description of cosmologies where no observer has access to the full spacetime.

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arXiv2012

The Gravity Dual of a Density Matrix

For a state in a quantum field theory on some spacetime, we can associate a density matrix to any subset of a given spacelike slice by tracing out the remaining degrees of freedom. In the context of the AdS/CFT correspondence, if the original state has a dual bulk spacetime with a good classical description, it is natural to ask how much information about the bulk spacetime is carried by the density matrix for such a subset of field theory degrees of freedom. In this note, we provide several constraints on the largest region that can be fully reconstructed, and discuss specific proposals for the geometric construction of this dual region.

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arXiv2011

Momentum-space entanglement and renormalization in quantum field theory

The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation between this density matrix and the conventional Wilsonian effective action. We argue that the entanglement entropy of and mutual information between subsets of field theoretic degrees of freedom at different momentum scales are natural observables in quantum field theory and demonstrate how to compute these in perturbation theory. The results may be understood heuristically based on the scale-dependence of the coupling strength and number of degrees of freedom. We measure the rate at which entanglement between degrees of freedom declines as their scales separate and suggest that this decay is related to the property of decoupling in quantum field theory.

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arXiv2011

Towards A Holographic Model of Color Superconductivity

In this note, we discuss the basic elements that should appear in a gravitational system dual to a confining gauge theory displaying color superconductivity at large baryon density. We consider a simple system with these minimal elements, and show that for a range of parameters, the phase structure of this model as a function of temperature and baryon chemical potential exhibits phases that can be identified with confined, deconfined, and color superconducting phases in the dual field theory. We find that the critical temperature at which the superconducting phase disappears is remarkably small (relative to the chemical potential). This small number arises from the dynamics, and is unrelated to any small parameter in the model that we study. We discuss similar models which exhibit flavor superconductivity.

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arXiv2011

Acceleration-Induced Deconfinement Transitions in de Sitter Spacetime

In this note, we consider confining gauge theories in $D=2,3,4$ defined by $S^2$ or $T^2$ compactification of higher-dimensional conformal field theories with gravity duals. We investigate the behavior of these theories on de Sitter spacetime as a function of the Hubble parameter. We find that in each case, the de Sitter vacuum state of the field theory (defined by Euclidian continuation from a sphere) undergoes a deconfinement transition as the Hubble parameter is increased past a critical value. In each case, the corresponding critical de Sitter temperature is smaller than the corresponding Minkowski-space deconfinement temperature by a factor nearly equal to the dimension of the de Sitter spacetime. The behavior is qualitatively and quantitatively similar to that for confining theories defined by $S^1$ compactification of CFTs, studied recently in arXiv:1007.3996.

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arXiv2010

Holographic models of de Sitter QFTs

We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show the such states make sense from the holographic viewpoint in that they have regular bulk gravity solutions. In the latter situation we add to the evidence for a confinement/deconfinement transition for a large N planar gauge theory as the cosmological acceleration is increased past a critical value. For the field theories we study, the critical acceleration corresponds to a de Sitter temperature which is less than the Minkowski space deconfinement transition temperature by a factor of the spacetime dimension.

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arXiv2010

Twisted Inflation

We present a new mechanism for slow-roll inflation based on higher dimensional supersymmetric gauge theory compactified to four dimensions with twisted (supersymmetry breaking) boundary conditions. These boundary conditions lead to a potential for directions in field space that would have been flat were supersymmetry preserved. For field values in these directions much larger than the supersymmetry-breaking scale, the flatness of the potential is nearly restored. Starting in this nearly flat region, inflation can occur as the theory relaxes towards the origin of field space. Near the origin, the potential becomes steep and the theory quickly descends to a confining gauge theory in which the inflaton does not exist as a particle. This confining gauge theory could be part of the Standard Model (QCD) or a natural dark matter sector; we comment on various scenarios for reheating. As a specific illustration of this mechanism, we discuss 4+1 dimensional maximally supersymmetric gauge theory on a circle with antiperiodic boundary conditions for fermions. When the theory is weakly coupled at the compactification scale, we calculate the inflaton potential directly in field theory by integrating out the heavy W-bosons and their superpartners. At strong coupling the model can be studied using a gravity dual, which realizes a new model of brane inflation on a non-supersymmetric throat geometry. Assuming there exists a UV completion that avoids the eta-problem, predictions from our model are consistent with present observations, and imply a small tensor-to-scalar ratio.

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arXiv2010

Baryon charge from embedding topology and a continuous meson spectrum in a new holographic gauge theory

We study a new holographic gauge theory based on probe D4-branes in the background dual to D4-branes on a circle with antiperiodic boundary conditions for fermions. Field theory configurations with baryons correspond to smooth embeddings of the probe D4-branes with nontrivial winding around an S^4 in the geometry. As a consequence, physics of baryons and nuclei can be studied reliably in this model using the abelian Born-Infeld action. However, surprisingly, we find that the meson spectrum is not discrete. This is related to a curious result that the action governing small fluctuations of the gauge field on the probe brane is the five-dimensional Maxwell action in Minkowski space despite the non-trivial embedding of the probe brane in the curved background geometry.

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arXiv2010

Comments on quantum gravity and entanglement

In this note, we attempt to provide some insights into the structure of non-perturbative descriptions of quantum gravity using known examples of gauge-theory / gravity duality. We argue that in familiar examples, a quantum description of spacetime can be associated with a manifold-like structure in which particular patches of spacetime are associated with states or density matrices in specific quantum systems. We argue that quantum entanglement between microscopic degrees of freedom plays an essential role in the emergence of a dual spacetime from the nonperturbative degrees of freedom. In particular, in at least some cases, classically connected spacetimes may be understood as particular quantum superpositions of disconnected spacetimes.

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arXiv2008

Cold Nuclear Matter In Holographic QCD

We study the Sakai-Sugimoto model of holographic QCD at zero temperature and finite chemical potential. We find that as the baryon chemical potential is increased above a critical value, there is a phase transition to a nuclear matter phase characterized by a condensate of instantons on the probe D-branes in the string theory dual. As a result of electrostatic interactions between the instantons, this condensate expands towards the UV when the chemical potential is increased, giving a holographic version of the expansion of the Fermi surface. We argue based on properties of instantons that the nuclear matter phase is necessarily inhomogeneous to arbitrarily high density. This suggests an explanation of the "chiral density wave" instability of the quark Fermi surface in large N_c QCD at asymptotically large chemical potential. We study properties of the nuclear matter phase as a function of chemical potential beyond the transition and argue in particular that the model can be used to make a semi-quantitative prediction of the binding energy per nucleon for nuclear matter in ordinary QCD.

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arXiv2008

A Massive Study of M2-brane Proposals

We test the proposals for the worldvolume theory of M2-branes by studying its maximally supersymmetric mass-deformation. We check the simplest prediction for the mass-deformed theory on N M2-branes: that there should be a set of discrete vacua in one-to-one correspondence with partitions on N. For the mass-deformed Lorentzian three-algebra theory, we find only a single classical vacuum, casting doubt on its M2-brane interpretation. For the mass-deformed ABJM theory, we do find a discrete set of solutions, but these are more numerous than predicted. We discuss possible resolutions of this puzzling discrepancy. We argue that the classical vacuum solutions of the mass-deformed ABJM theory display properties of fuzzy three-spheres, as expected from their gravitational dual interpretation.

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arXiv2008

Supersymmetric Yang-Mills Theory From Lorentzian Three-Algebras

We show that by adding a supersymmetric Faddeev-Popov ghost sector to the recently constructed Bagger-Lambert theory based on a Lorentzian three algebra, we obtain an action with a BRST symmetry that can be used to demonstrate the absence of negative norm states in the physical Hilbert space. We show that the combined theory, expanded about its trivial vacuum, is BRST equivalent to a trivial theory, while the theory with a vev for one of the scalars associated with a null direction in the three-algebra is equivalent to a reformulation of maximally supersymmetric 2+1 dimensional Yang-Mills theory in which there a formal SO(8) superconformal invariance.

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arXiv2008

M2-branes on M-folds

We argue that the moduli space for the Bagger-Lambert A_4 theory at level k is (R^8 \times R^8)/D_{2k}, where D_{2k} is the dihedral group of order 4k. We conjecture that the theory describes two M2-branes on a Z_{2k} ``M-fold'', in which a geometrical action of Z_{2k} is combined with an action on the branes. For k=1, this arises as the strong coupling limit of two D2-branes on an O2^- orientifold, whose worldvolume theory is the maximally supersymmetric SO(4) gauge theory. Finally, in an appropriate large-k limit we show that one recovers compactified M-theory and the M2-branes reduce to D2-branes.

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arXiv2008

Comments on the Bagger-Lambert theory and multiple M2-branes

We study the SO(8) superconformal theory proposed recently by Bagger and Lambert as a possible worldvolume theory for multiple M2-branes. For their explicit example with gauge group SO(4), we rewrite the theory (originally formulated in terms of a three-algebra) as an ordinary SU(2) \times SU(2) gauge theory with bifundamental matter. In this description, the parity invariance of the theory, required for a proper description of M2-branes, is clarified. We describe the subspace of scalar field configurations on which the potential vanishes, and note that this does not coincide with the moduli space for a stack of M2-branes. Finally, we point out a difficulty in constructing the required set of superconformal primary operators which should be present in the correct theory describing multiple M2-branes.

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arXiv2008

Black Hole Dynamics From Atmospheric Science

In this note, we derive (to third order in derivatives of the fluid velocity) a 2+1 dimensional theory of fluid dynamics that governs the evolution of generic long-wavelength perturbations of a black brane or large black hole in four-dimensional gravity with negative cosmological constant, applying a systematic procedure developed recently by Bhattacharyya, Hubeny, Minwalla, and Rangamani. In the regime of validity of the fluid-dynamical description, the black-brane evolution will generically correspond to a turbulent flow. Turbulence in 2+1 dimensions has been well studied analytically, numerically, experimentally, and observationally as it provides a first approximation to the large scale dynamics of planetary atmospheres. These studies reveal dramatic differences between fluid flows in 2+1 and 3+1 dimensions, suggesting that the dynamics of perturbed four and five dimensional large AdS black holes may be qualitatively different. However, further investigation is required to understand whether these qualitative differences exist in the regime of fluid dynamics relevant to black hole dynamics.

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arXiv2007

Coarse-Graining the Lin-Maldacena Geometries

The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.

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arXiv2007

A second order deconfinement transition for large N 2+1 dimensional Yang-Mills theory on a small two-sphere

We study the thermodynamics of large N pure 2+1 dimensional Yang-Mills theory on a small spatial sphere. By studying the effective action for the Polyakov loop order parameter, we show analytically that the theory has a second order deconfinement transition to a phase where the eigenvalue distribution of the Polyakov loop is non-uniform but still spread over the whole unit circle. At a higher temperature, the eigenvalue distribution develops a gap, via an additional third-order phase transition. We discuss possible forms of the full phase diagram as a function of temperature and sphere radius. Our results together with extrapolation of lattice results relevant to the large volume limit imply the existence of a critical radius in the phase diagram at which the deconfinement transition switches from second order to first order. We show that the point at the critical radius and temperature can be either a tricritical point with universal behavior or a triple point separating three distinct phases.

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arXiv2007

Transverse Fivebranes in Matrix Theory

M-theory on the maximally supersymmetric plane wave background of eleven-dimensional supergravity admits spherical BPS transverse M5-branes with zero light-cone energy. We give direct evidence that the single M5-brane state corresponds to the trivial (X=0) classical vacuum in the large N limit of the plane wave matrix theory. In particular, we show that the linear fluctuation spectrum of the spherical fivebrane matches exactly with the set of exactly protected excited states about the X=0 vacuum in the matrix model. These states include geometrical fluctuations of the sphere, excitations of the worldvolume two-form field, and fermion excitations. In addition, we propose a description of multiple fivebrane states in terms of matrix model vacua. Finally, we discuss how to obtain the continuum D2/M2 and NS5/M5 theories on spheres from the matrix model. The matrix model can be viewed as a regularization for these theories.

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