arXiv subjects

Vijay Balasubramanian

Publications and source records attributed to Vijay Balasubramanian.

At least 163 records · Page 9Linked to original sources

arXiv2001

Supersymmetric Conical Defects: Towards a string theoretic description of black hole formation

Conical defects, or point particles, in AdS_3 are one of the simplest non-trivial gravitating systems, and are particularly interesting because black holes can form from their collision. We embed the BPS conical defects of three dimensions into the N=4b supergravity in six dimensions, which arises from IIB string theory compactified on K3. The required Kaluza-Klein reduction of the six dimensional theory on a sphere is analyzed in detail, including the relation to the Chern-Simons supergravities in three dimensions. We show that the six dimensional spaces obtained by embedding the 3d conical defects arise in the near-horizon limit of rotating black strings. Various properties of these solutions are analyzed and we propose a representation of our defects in the CFT dual to asymptotically AdS_3 x S^3 spaces. Our work is intended as a first step towards analyzing colliding defects that form black holes.

hep-th↗

arXiv2000

Four Dimensional Conformal Supergravity From AdS Space

Exploring the role of conformal theories of gravity in string theory, we show that the minimal (N=2) gauged supergravities in five dimensions induce the multiplets and transformations of N=1 four dimensional conformal supergravity on the spacetime boundary. N=1 Poincare supergravity can be induced by explicitly breaking the conformal invariance via a radial cutoff in the 5d space. The AdS/CFT correspondence relates the maximal gauged supergravity in five dimensions to N=4 super Yang-Mills on the 4d spacetime boundary. In this context we show that the conformal anomaly of the gauge theory induces conformal gravity on the boundary of the space and that this theory, via the renormalization group, encapsulates the gravitational dynamics of the skin of asymptotically AdS spacetimes. Our results have several applications to the AdS/CFT correspondence and the Randall-Sundrum scenario.

hep-th↗

arXiv2000

Consistency Conditions for Holographic Duality

We show that if the beta functions of a field theory are given by the gradient of a certain potential on the space of couplings, a gravitational background in one more dimension can express the renormalization group (RG) flow of the theory. The field theory beta functions and the gradient flow constraint together reconstruct the second order spacetime equations of motion. The RG equation reduces to the conventional gravitational computation of the spacetime quasilocal stress tensor, and a c-theorem holds true as a consequence of the Raychaudhuri equation. Conversely, under certain conditions, if the RG evolution of a field theory possesses a monotonic c-function, the flow of couplings can be expressed in terms of a higher dimensional gravitational background.

hep-th↗

arXiv1999

A Stress Tensor for Anti-de Sitter Gravity

We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS_5, and show that it exactly matches the Casimir energy of the dual N=4 super Yang-Mills theory on S^3 x R.

hep-th↗

arXiv1999

Holographic Particle Detection

In anti-de Sitter (AdS) space, classical supergravity solutions are represented "holographically" by conformal field theory (CFT) states in which operators have expectation values. These 1-point functions are directly related to the asymptotic behaviour of bulk fields. In some cases, distinct supergravity solutions have identical asymptotic behaviour; so dual expectation values are insufficient to distinguish them. We argue that non-local objects in the gauge theory can resolve the ambiguity, and explicitly show that collections of point particles in AdS_3 can be detected by studying kinks in dual CFT Green functions. Three dimensional black holes can be formed by collision of such particles. We show how black hole formation can be detected in the holographic dual, and calculate CFT quantities that are sensitive to the distribution of matter inside the event horizon.

hep-th↗

arXiv1999

Spacetime and the Holographic Renormalization Group

Anti-de Sitter (AdS) space can be foliated by a family of nested surfaces homeomorphic to the boundary of the space. We propose a holographic correspondence between theories living on each surface in the foliation and quantum gravity in the enclosed volume. The flow of observables between our ``interior'' theories is described by a renormalization group equation. The dependence of these flows on the foliation of space encodes bulk geometry.

hep-th↗

arXiv1999

What Do CFTs Tell Us About Anti-de Sitter Spacetimes?

The AdS/CFT conjecture relates quantum gravity on Anti-de Sitter (AdS) space to a conformal field theory (CFT) defined on the spacetime boundary. We interpret the CFT in terms of natural analogues of the bulk S-matrix. Our first approach finds the bulk S-matrix as a limit of scattering from an AdS bubble immersed in a space admitting asymptotic states. Next, we show how the periodicity of geodesics obstructs a standard LSZ prescription for scattering within global AdS. To avoid this subtlety we partition global AdS into patches within which CFT correlators reconstruct transition amplitudes of AdS states. Finally, we use the AdS/CFT duality to propose a large N collective field theory that describes local, perturbative supergravity. Failure of locality in quantum gravity should be related to the difference between the collective 1/N expansion and genuine finite N dynamics.

hep-th↗

arXiv1998

The Spin of the M2-Brane and Spin-Spin Interactions via Probe Techniques

The 256 dimensional M2-brane multiplet contains solitons of many different intrinsic spins. Using the broken supersymmetry transformations of the M2-brane, we find supergravity solutions which explicitly display these spins. This amounts to quantizing the fermionic zero modes and computing the back reaction on the metric and gauge potential. These spacetime fields are therefore operator valued and acquire a conventional classical meaning only after taking expectations in given BPS states. Our spinning spacetimes are not of the standard Kerr form -- there is a non-vanishing gravitino. Nevertheless, the solutions have angular momentum and magnetic dipole moments with a g-factor of 2. We use probe techniques to study scattering of spinning BPS M2-branes. The static interactions cancel between like-sign branes at leading order, but there are static spin-spin forces between branes and anti-branes. The general probe-background Lagrangian contains gravitational spin-spin and magnetic dipole-dipole forces, as well as gravitino exchanges which allow branes to change fermion number.

hep-th↗

arXiv1998

Holographic Probes of Anti-de Sitter Spacetimes

We describe probes of anti-de Sitter spacetimes in terms of conformal field theories on the AdS boundary. Our basic tool is a formula that relates bulk and boundary states -- classical bulk field configurations are dual to expectation values of operators on the boundary. At the quantum level we relate the operator expansions of bulk and boundary fields. Using our methods, we discuss the CFT description of local bulk probes including normalizable wavepackets, fundamental and D-strings, and D-instantons. Radial motions of probes in the bulk spacetime are related to motions in scale on the boundary, demonstrating a scale-radius duality. We discuss the implications of these results for the holographic description of black hole horizons in the boundary field theory.

hep-th↗

arXiv1998

Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime

We investigate the details of the bulk-boundary correspondence in Lorentzian signature anti-de Sitter space. Operators in the boundary theory couple to sources identified with the boundary values of non-normalizable bulk modes. Such modes do not fluctuate and provide classical backgrounds on which bulk excitations propagate. Normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition. They fluctuate and describe the Hilbert space of physical states. We provide an explicit, complete set of both types of modes for free scalar fields in global and Poincaré coordinates. For $\ads{3}$, the normalizable and non-normalizable modes originate in the possible representations of the isometry group $\SL_L\times\SL_R$ for a field of given mass. We discuss the group properties of mode solutions in both global and Poincaré coordinates and their relation to different expansions of operators on the cylinder and on the plane. Finally, we discuss the extent to which the boundary theory is a useful description of the bulk spacetime.

hep-th↗

arXiv1997

How To Count the States of Extremal Black Holes in N=8 Supergravity

N=8 supergravity has a rich spectrum of black holes charged under the 56 U(1) gauge fields of the theory. Duality predicts that the entropy of these black holes is related to the quartic invariant of the E(7,7) group. We verify this prediction in detail by constructing black holes that correspond to supersymmetric bound states of 2-branes at angles and 6-branes. The general bound state contains an arbitrary number of branes rotated relative to each other, and we derive the condition for these rotations to preserve supersymmetry. The microscopic bound state degeneracy matches the black hole entropy in detail. The entire 56 charge spectrum of extremal black holes in N=8 supergravity can be displayed as the orbit under duality of a five parameter generating solution. We exhibit a new generating configuration consisting of D3-branes at angles and discuss its entropy.

hep-th↗

arXiv1997

Relativistic Brane Scattering

We calculate relativistic phase-shifts resulting from the large impact parameter scattering of 0-branes off p-branes within supergravity. Their full functional dependence on velocity agrees with that obtained by identifying the p-branes with D-branes in string theory. These processes are also described by 0-brane quantum mechanics, but only in the non-relativistic limit. We show that an improved 0-brane quantum mechanics based on a Born-Infeld type Lagrangian also does not yield the relativistic results. Scattering of 0-branes off bound states of arbitrary numbers of 0-branes and 2-branes is analyzed in detail, and we find agreement between supergravity and string theory at large distances to all orders in velocity. Our careful treatment of this system, which embodies the 11 dimensional kinematics of 2-branes in M(atrix) theory, makes it evident that control of 1/n corrections will be necessary in order to understand our relativistic results within M(atrix) theory.

hep-th↗

arXiv1997

Extremal Branes as Elementary Particles

The supersymmetric p-branes of Type II string theory can be interpreted after compactification as extremal black holes with zero entropy and infinite temperature. We show how the p-branes avoid this apparent, catastrophic instability by developing an infinite mass gap. Equivalently, these black holes behave like elementary particles: they are dressed by effective potentials that prevent absorption of impinging particles. In contrast, configurations with 2, 3, and 4 intersecting branes and their nonextremal extensions, behave increasingly like conventional black holes. These results extend and clarify earlier work by Holzhey and Wilczek in the context of four dimensional dilaton gravity.

hep-th↗

arXiv1997

D-Branes, Moduli and Supersymmetry

We study toroidal compactifications of Type II string theory with D-branes and nontrivial antisymmetric tensor moduli and show that turning on these fields modifies the supersymmetry projections imposed by D-branes. These modifications are seen to be necessary for the consistency of T-duality. We also show the existence of unusual BPS configurations of branes at angles that are supersymmetric because of conspiracies between moduli fields. Analysis of the problem from the point of view of the effective field theory of massless modes shows that the presence of a 2-form background must modify the realization of supersymmetry on the brane. In particular, the appropriate supersymmetry variation of the physical gaugino vanishes in any constant field strength background. These considerations are relevant for the $E_7$-symmetric counting of states of 4-dimensional black holes in Type II string theory compactified on $T^6$.

hep-th↗

arXiv1996

Some Aspects of Massive World-Brane Dynamics

We study the internal dynamics of Ramond-Ramond solitons excited far from the BPS limit by leading Regge trajectory open strings. The simplest world volume process for such strings is splitting into two smaller pieces, and we calculate the corresponding decay rates. Compared to the conventional open superstring, the splitting of states polarized parallel to the brane is suppressed by powers of logarithms of the energy. The rate for states polarized transverse to the brane {\em decreases} with increasing energy. We also calculate the static force between a D-brane excited by a massive open string and an unexcited D-brane parallel to it. The result shows that transversely polarized massive open strings endow D-branes with a size of order the string scale.

hep-th↗

arXiv1996

On D-Branes and Black Holes in Four Dimensions

We find extremal four dimensional black holes with finite area constructed entirely from intersecting D-branes. We argue that the microscopic degeneracy of these configurations agrees with the Bekenstein-Hawking entropy formula. The absence of solitonic objects in these configurations may make them useful for dynamical studies of black holes.

hep-th↗

arXiv1996

Back-Reaction and Complementarity in 1+1 Dilaton Gravity

We study radiation from black holes in the effective theory produced by integrating gravity and the dilaton out of $1+1$ dilaton gravity. The semiclassical wavefunctions for the dressed particles show that the self-interactions produce an unusual renormalization of the frequencies of outgoing states. Modes propagating in the dynamical background of an incoming quantum state are seen to acquire large scattering phases that nevertheless conspire, in the absence of self-interactions, to preserve the thermality of the Hawking radiation. However, the in-out scattering matrix does not commute with the self-interactions and this could lead to observable corrections to the final state. Finally, our calculations explicitly display the limited validity of the semiclassical theory of Hawking radiation and provide support for a formulation of black hole complementarity.

hep-th↗

arXiv1996

Statistical Inference, Occam's Razor and Statistical Mechanics on The Space of Probability Distributions

The task of parametric model selection is cast in terms of a statistical mechanics on the space of probability distributions. Using the techniques of low-temperature expansions, we arrive at a systematic series for the Bayesian posterior probability of a model family that significantly extends known results in the literature. In particular, we arrive at a precise understanding of how Occam's Razor, the principle that simpler models should be preferred until the data justifies more complex models, is automatically embodied by probability theory. These results require a measure on the space of model parameters and we derive and discuss an interpretation of Jeffreys' prior distribution as a uniform prior over the distributions indexed by a family. Finally, we derive a theoretical index of the complexity of a parametric family relative to some true distribution that we call the {\it razor} of the model. The form of the razor immediately suggests several interesting questions in the theory of learning that can be studied using the techniques of statistical mechanics.

cond-mat↗