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Leonard Susskind

Publications and source records attributed to Leonard Susskind.

At least 127 records · Page 7Linked to original sources
arXiv1999

Negative Energy, Superluminosity and Holography

The holographic connection between large $N$ Super Yang Mills theory and gravity in anti deSitter space requires unfamiliar behavior of the SYM theory in the limit that the curvature of the AdS geometry becomes small. The paradoxical behavior includes superluminal oscillations and negative energy density. These effects typically occur in the SYM description of events which take place far from the boundary of AdS when the signal from the event arrives at the boundary. The paradoxes can be resolved by assuming a very rich collection of hidden degrees of freedom of the SYM theory which store information but give rise to no local energy density. These degrees of freedom, called precursors, are needed to make possible sudden apparently acausal energy momentum flows. Such behavior would be impossible in classical field theory as a consequence of the positivity of the energy density. However we show that these effects are not only allowed in quantum field theory but that we can model them in free quantum field theory.

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arXiv1999

Holography in the Flat Space Limit

Matrix theory and the AdS/CFT correspondence provide nonperturbative holographic formulations of string theory. In both cases the finite N theories can be thought of as infrared regulated versions of flat space string theory in which removing the cutoff is equivalent to letting N go to infinity. In this paper we consider the nature of this limit. In both cases the holographic mapping becomes completely nonlocal. In matrix theory this corresponds to the growth of D0-brane bound states with N. For the AdS/CFT correspondence there is a similar delocalization of the holographic image of a system as N increases. In this case the limiting theory seems to require a number of degrees of freedom comparable to large N matrix quantum mechanics.

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arXiv1998

Large N and the Dine-Rajaraman problem

We compute the effective action for scattering of three well-separated extremal brane solutions, in 11d supergravity, with zero p_ transfer and small transverse velocities. Using an interpretation of the conjecture of Maldacena, following Hyun, this can be viewed as the large N limit of the Matrix theory description of three supergraviton scattering at leading order. The result is consistent with the perturbative supergravity calculation.

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arXiv1997

Review of Matrix Theory

In this article we present a self contained review of the principles of Matrix Theory including the basics of light cone quantization, the formulation of 11 dimensional M-Theory in terms of supersymmetric quantum mechanics, the origin of membranes and the rules of compactification on 1,2 and 3 tori. We emphasize the unusual origins of space time and gravitation which are very different than in conventional approaches to quantum gravity. Finally we discuss application of Matrix Theory to the quantum mechanics of Schwarzschild black holes. This work is based on lectures given by the second author at the Cargese ASI 1997 and at the Institute for Advanced Study in Princeton.

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arXiv1997

A note on discrete light cone quantization

In this brief note we would like to discuss, in a simple model system, the conditions under which the discrete light cone quantization framework should be trusted as an approximation scheme, with regard, in particular, to the size and mass of the system. Specifically, we are going to discuss ``quark-antiquark'' bound states in 1+1 dim., for which a natural size is provided by analogy with a ``two points and a spring'' system, and show that the condition for obtaining a reliable estimate is the same as the one derived in a recent paper for black holes in matrix theory.

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arXiv1997

Schwarzschild Black Holes in Various Dimensions from Matrix Theory

In a recent paper it was shown that the properties of Schwarzschild black holes in 8 dimensions are correctly described up to factors of order unity by Matrix theory compactified on T^3. Here we consider compactifications on tori of general dimension d. Although in general little is known about the relevant d+1 dimensional theories on the dual tori, there are hints from their application to near-extreme parallel Dirichlet d-branes. Using these hints we get the correct mass-entropy scaling for Schwarzschild black holes in (11-d) dimensions.

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arXiv1997

Finite N Heterotic Matrix Models and Discrete Light Cone Quantization

The finite N version of Matrix theory describes M-theory and superstrings in so-called discretized light cone quantization (DLCQ). Its role has been explained for M-theory in 11 dimensions and for type IIA theory. We show novelties which arise by generalizing the ideas to heterotic strings. The states which arise in O(N) theories with odd N we interpret as fields which are antiperiodic in the longitudinal direction. Consistency of these ideas provides a new evidence for the conjecture that finite N models describe sectors with a given longitudinal momentum.

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arXiv1997

Another Conjecture about M(atrix) Theory

The current understanding of M(atrix) theory is that in the large N limit certain supersymmetric Yang Mills theories become equivalent to M-theory in the infinite momentum frame. In this paper the conjecture is put forward that the equivalence between M and M(atrix) theory is not limited to the large N limit but is valid for finite N. It is argued that a light cone description of M-theory exists in which one of the light like coordinates is periodically identified. In the light cone literature this is called Discrete Light Cone Quantization (DLCQ). In this framework an exact light cone description exists for each quantized value N of longitudinal momentum. The new conjecture states that the sector of the DLCQ of M-theory is exactly described by a U(N) matrix theory. Evidence is presented for the conjecture.

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arXiv1997

Rotational Invariance in the M(atrix) Formulation of Type IIB Theory

The matrix model formulation of M-theory can be generalized by compactification to ten-dimensional type II string theory, formulated in the infinite momentum frame. Both the type IIA and IIB string theories can be formulated in this way. In the M-theory and type IIA cases, the transverse rotational invariance is manifest, but in the IIB case, one of the transverse dimensions materializes in a completely different way from the other seven. The full O(8) rotational symmetry then follows in a surprising way from the electric-magnetic duality of supersymmetric Yang-Mills field theory.

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arXiv1996

T Duality in M(atrix) Theory and S Duality in Field Theory

The matrix model formulation of M theory can be generalized to compact transverse backgrounds such as tori. If the number of compact directions is K then the matrix model must be generalized to K+1 dimensional super Yang Mills theory on a compact space. If K is greater than or equal to 3, there are T dualities which which require highly nontrivial identifications between different SYM theories. In the simplest case we will see that the requirement reduces to the well known electric- magnetic duality of N=4 SYM theory in 3+1 dimensions.

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arXiv1996

D-branes and Fat Black Holes

The application of D-brane methods to large black holes whose Schwarzschild radius is larger than the compactification scale is problematic. Callan and Maldacena have suggested that despite apparent problems of strong interactions when the number of branes becomes large, the open string degrees of freedom may remain very dilute due to the growth of the horizon area which they claim grows more rapidly than the average number of open strings. Such a picture of a dilute weakly coupled string system conflicts with the picture of a dense string-soup that saturates the bound of one string per planck area. A more careful analysis shows that Callan and Maldacena were not fully consistent in their estimates. In the form that their model was studied it can not be used to extrapolate to large mass without being in conflict with the Hawking Bekenstein entropy formula. A somewhat modified model can reproduce the correct entropy formula. In this ``improved model" the number of string bits on the horizon scales like the entropy in agreement with earlier speculations of Susskind.

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arXiv1995

String Physics and Black Holes

In these lectures we review the quantum physics of large Schwarzschild black holes. Hawking's information paradox, the theory of the stretched horizon and the principle of black hole complementarity are covered. We then discuss how the ideas of black hole complementarity may be realized in string theory. Finally, arguments are given that the world may be a hologram. Lectures delivered at ICTP Spring School on String Theory, Gauge Theory, and Quantum Gravity, 1995.

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arXiv1995

Supersymmetric Balance of Forces and Condensation of BPS States

Until now all known static multi black hole solutions described BPS states with charges of the same sign. Such solutions could not be related to flat directions in the space of BPS states. The total number of such states could not spontaneously increase because of the charge conservation. We show that there exist static BPS configurations which remain in equilibrium even if they consist of states with opposite electric (or magnetic) charges from vector multiplets. This is possible because of the exact cancellation between the Coulomb and scalar forces. In particular, in the theories with N=4 or N=2 supersymmetry there exist stable massless multi center configurations with vanishing total charge. Since such configurations have vanishing energy and charge independently of their number, they can be associated with flat directions in the space of all possible BPS states. For N=2 case this provides a realization of the idea that BPS condensates could relate to each other different vacua of the string theory.

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arXiv1995

Black Hole Complementarity vs. Locality

The evaporation of a large mass black hole can be described throughout most of its lifetime by a low-energy effective theory defined on a suitably chosen set of smooth spacelike hypersurfaces. The conventional argument for information loss rests on the assumption that the effective theory is a local quantum field theory. We present evidence that this assumption fails in the context of string theory. The commutator of operators in light-front string theory, corresponding to certain low-energy observers on opposite sides of the event horizon, remains large even when these observers are spacelike separated by a macroscopic distance. This suggests that degrees of freedom inside a black hole should not be viewed as independent from those outside the event horizon. These nonlocal effects are only significant under extreme kinematic circumstances, such as in the high-redshift geometry of a black hole. Commutators of space-like separated operators corresponding to ordinary low-energy observers in Minkowski space are strongly suppressed in string theory.

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arXiv1995

GRAVITY AND GLOBAL SYMMETRIES

There exists a widely spread notion that gravitational effects can strongly violate global symmetries. It may lead to many important consequences. We will argue, in particular, that nonperturbative gravitational effects in the axion theory lead to a strong violation of CP invariance unless they are suppressed by an extremely small factor 10^{-82}. One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar axion field as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tensor field. We will show, however, that this gauge symmetry does not protect the axion mass from quantum corrections. The amplitude of gravitational effects violating global symmetries could be strongly suppressed by e^{-S}, where S is the action of a wormhole which may eat the global charge. Unfortunately, in a wide variety of theories based on the Einstein theory of gravity the action appears to be fairly small, S = O(10). However, we have found that the existence of wormholes and the value of their action are extremely sensitive to the structure of space on the nearly Planckian scale. We consider several examples (Kaluza-Klein theory, conformal anomaly, R^2 terms) which show that modifications of the Einstein theory on the length scale l ~ 10 M_P^{-1} may strongly suppress violation of global symmetries. We have found also that in string theory there exists an additional suppression of topology change by the factor e^{-{8π^2\over g^2}}. This effect is strong enough to save the axion theory for the natural values of the stringy gauge coupling constant.

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arXiv1995

Trouble For Remnants

An argument is presented for the inconsistency of black hole remnants which store the information which falls into black holes. Unlike previous arguments it is not concerned with a possible divergence in the rate of pair production. It is argued that the existence of remnants in the thermal atmosphere of Rindler space will drive the renormalized Newton constant to zero.

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arXiv1994

Comment On A Proposal By Strominger

Strominger has proposed an interesting concrete realization of Hawking's idea that information is lost in black hole evaporation. In this note we demonstrate that a straightforward interpretation of Strominger's model leads to a complete breakdown of the conditions for using statistics for analyzing the results of experiments. The probabilities produced by the theory are operationally meaningless.

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