Searcharxiv⌕ Search

arXiv subjects

L. Susskind

Publications and source records attributed to L. Susskind.

At least 19 recordsLinked to original sources
arXiv2002

Proceedings to the Workshops ''What comes beyond the Standard model'' 2000,2001, VOLUME 1: Festschrift dedicated to the 60th birthday of Holger Bech Nielsen

The present volume is the collection of contributions by friends of Holger Bech Nielsen for his 60th birthday. Contents: 1.Unified internal space of spins and charges (N. Mankoc Borstnik) 2.Semitopological Q-Rings (M. Axenides) 3.Non-local axial anomalies in the Standard model (D. Melikhov, B. Stech) 4.Could there be a fourth generation? (C.D. Froggatt) 5.Another complex Bateman equation (D.B. Fairlie) 6.Non-associative loops for Holger Bech Nielsen (P.H. Frampton) 7.Particles, fluids and vortices (J.W. van Holten) 8.Results on 2D current algebras (J.L. Petersen) 9.Phase transition in gauge theories and the Planck scale physics (L.V. Laperashvili and D.A. Ryzhikh) 10.Some remarks on the 'classical' large N limit (P. Olesen) 11.String theory and the size of hadrons (L. Susskind) 12.Relativity and $c/sqrt3$ (S.I. Blinnikov, L.B. Okun and M.I. Vysotsky) 13.Vortices (Jeff Greensite)

hep-ph↗
arXiv2001

The Quantum Hall Fluid and Non-Commutative Chern Simons Theory

The first part of this paper is a review of the author's work with S. Bahcall which gave an elementary derivation of the Chern Simons description of the Quantum Hall effect for filling fraction $1/n$. The notation has been modernized to conform with standard gauge theory conventions. In the second part arguments are given to support the claim that abelian non-commutative Chern Simons theory at level $n$ is exactly equivalent to the Laughlin theory at filling fraction $1/n$. The theory may also be formulated as a matrix theory similar to that describing D0-branes in string theory. Finally it can also be thought of as the quantum theory of mappings between two non-commutative spaces, the first being the target space and the second being the base space.

hep-th↗
arXiv2000

How Bob Laughlin Tamed the Giant Graviton from Taub-NUT space

In this paper we show how two dimensional electron systems can be modeled by strings interacting with D-branes. The dualities of string theory allow several descriptions of the system. These include descriptions in terms of solitons in the near horizon D6-brane theory, non-commutative gauge theory on a D2-brane, the Matrix Theory of D0-branes and finally as a giant graviton in M-theory. The soliton can be described as a D2-brane with an incompressible fluid of D0-branes and charged string-ends moving on it. Including an NS5 brane in the system allows for the existence of an edge with the characteristic massless chiral edge states of the Quantum Hall system.

hep-th↗
arXiv2000

Space/Time Non-Commutativity and Causality

Field theories based on non-commutative spacetimes exhibit very distinctive nonlocal effects which mix the ultraviolet with the infrared in bizarre ways. In particular if the time coordinate is involved in the non-commutativity the theory seems to be seriously acausal and inconsistent with conventional Hamiltonian evolution. To illustrate these effects we study the scattering of wave packets in a field theory with space/time non-commutativity. In this theory we find effects which seem to precede their causes and rigid rods which grow instead of Lorentz contract as they are boosted. These field theories are evidently inconsistent and violate causality and unitarity. On the other hand open string theory in a background electric field is expected to exhibit space/time non-commutativity. This raises the question of whether they also lead to acausal behavior. We show that this is not the case. Stringy effects conspire to cancel the acausal effects that are present for the non-commutative field theory.

hep-th↗
arXiv2000

Strings in Background Electric Field, Space/Time Noncommutativity and A New Noncritical String Theory

Searching for space/time noncommutativity we reconsider open strings in a constant background electric field. The main difference between this situation and its magnetic counterpart is that here there is a critical electric field beyond which the theory does not make sense. We show that this critical field prevents us from finding a limit in which the theory becomes a field theory on a noncommutative spacetime. However, an appropriate limit toward the critical field leads to a novel noncritical string theory on a noncommutative spacetime.

hep-th↗
arXiv1998

Holography and Cosmology

A cosmological version of the holographic principle is proposed. Various consequences are discussed including bounds on equation of state and the requirement that the universe be infinite.

hep-th↗
arXiv1998

The Holographic Bound in Anti-de Sitter Space

The correspondence between string theory in Anti-de Sitter space and super Yang Mills theory is an example of the Holographic principle according to which a quantum theory with gravity must be describable by a boundary theory. However, arguments given so far are incomplete because, while the bulk theory has been related to a boundary theory, the holographic bound saying that the boundary theory has only one bit of information per Planck area has not been justified. We show here that this bound is the physical interpretation of one of the unusual aspects of the correspondence between Anti-de Sitter space and the boundary conformal field theory, which is that infrared effects in the bulk theory are reflected as ultraviolet effects in the boundary theory.

hep-th↗
arXiv1998

Matrix Theory Black Holes and the Gross Witten Transition

Large N gauge theories have so called Gross-Witten phase transitions which typically can occur in finite volume systems. In this paper we relate these transitions in supersymmetric gauge theories to transitions that take place between black hole solutions in general relativity. The correspondence between gauge theory and gravitation is through matrix theory which represents the gravitational system in terms of super Yang Mills theories on finite tori. We also discuss a related transition that was found by Banks, Fischler, Klebanov and Susskind.

hep-th↗
arXiv1997

Schwarzchild Black Holes in Matrix Theory II

We present a crude Matrix Theory model for Schwarzchild black holes in uncompactified dimension greater than $5$. The model accounts for the size, entropy, and long range state interactions of black holes. The key feature of the model is a Boltzmann gas of D0 branes, a concept which depends on certain qualitative features of Matrix Theory which have not previously been utilized in studies of black holes.

hep-th↗
arXiv1997

Schwarzschild Black Holes from Matrix Theory

We consider Matrix theory compactified on T^3 and show that it correctly describes the properties of Schwarzschild black holes in 7+1 dimensions, including the energy-entropy relation, the Hawking temperature and the physical size, up to numerical factors of order unity. The most economical description involves setting the cut-off N in the discretized light-cone quantization to be of order the black hole entropy. A crucial ingredient necessary for our work is the recently proposed equation of state for 3+1 dimensional SYM theory with 16 supercharges. We give detailed arguments for the range of validity of this equation following the methods of Horowitz and Polchinski.

hep-th↗
arXiv1997

Instantons, Scale Invariance and Lorentz Invariance in Matrix Theory

In this paper we consider features of graviton scattering in Matrix theory compactified on a 2-torus. The features which interest us can only be determined by nonperturbative effects in the corresponding 2+1 dimensional super Yang Mills theory. We show that the superconformal symmetry of strongly coupled Super Yang Mills Theory in 2+1 dimensions almost determines low energy, large impact parameter ten dimensional graviton scattering at zero longitudinal momentum in the Matrix model of IIB string theory. We then show that amplitudes involving arbitrary transverse momentum transfer are governed by instanton processes similar to the Polchinski Pouliot process. Finally we consider the influence of instantons on a conjectured nonrenormalization theorem. This theorem is violated by instanton processes. Far from being a problem, this fact is seen to be crucial to the consistency of the IIB interpretation. We suggest that the SO(8) invariance of strongly coupled SYM theory may lead to a proof of eleven dimensional Lorentz invariance.

hep-th↗
arXiv1997

The Incredible Shrinking Torus

Using M(atrix) Theory, the dualities of toroidally compactified M-theory can be formulated as properties of super Yang Mills theories in various dimensions. We consider the cases of compactification on one, two, three, four and five dimensional tori. The dualities required by string theory lead to conjectures of remarkable symmetries and relations between field theories as well as extremely unusual dynamical properties. By studying the theories in the limit of vanishingly small tori, a wealth of information is obtained about strongly coupled fixed points of super Yang-Mills theories in various dimensions. Perhaps the most striking behavior, as noted by Rozali in this context, is the emergence of an additional dimension of space in the case of a four torus.

hep-th↗
arXiv1997

M Theory As A Matrix Model: A Conjecture

We suggest and motivate a precise equivalence between uncompactified eleven dimensional M-theory and the N = infinity limit of the supersymmetric matrix quantum mechanics describing D0-branes. The evidence for the conjecture consists of several correspondences between the two theories. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the entire Fock space of massless well separated particles of the supergravity theory. In one particular kinematic situation the leading large distance interaction of these particles is exactly described by supergravity . The model appears to be a nonperturbative realization of the holographic principle. The membrane states required by M-theory are contained as excitations of the matrix model. The membrane world volume is a noncommutative geometry embedded in a noncommutative spacetime.

hep-th↗
arXiv1996

Counting Schwarzschild and Charged Black Holes

We review the arguments that fundamental string states are in one to one correspondence with black hole states. We demonstrate the power of the assumption by showing that it implies that the statistical entropy of a wide class of nonextreme black holes occurring in string theory is proportional to the horizon area. However, the numerical coefficient relating the area and entropy only agrees with the Bekenstein--Hawking formula if the central charge of the string is six which does not correspond to any known string theory. Unlike the current D-brane methods the method used in this paper is applicable for the case of Schwarzschild and highly non-extreme charged black holes.

hep-th↗
arXiv1996

Braneless Black Holes

It is known that the naive version of D-brane theory is inadequate to explain the black hole entropy in the limit in which the Schwarzschild radius becomes larger than all compactification radii. We present evidence that a more consistent description can be given in terms of strings with rescaled tensions. We show that the rescaling can be interpreted as a redshift of the tension of a fundamental string in the gravitational field of the black hole. An interesting connection is found between the string level number and the Rindler energy. Using this connection, we reproduce the entropies of Schwarzschild black holes in arbitrary dimensions in terms of the entropy of a single string at the Hagedorn temperature.

hep-th↗
arXiv1995

Brane - Anti-Brane Forces

The force between like sign BPS saturated objects generally vanishes. This is a reflection of the fact that BPS states are really massless uncharged particles with nonvanishing momenta in compactified directions. Two like sign BPS objects with zero relative velocity can be viewed as a boosted state of two neutral massless particles in a state of vanishing relative motion. By contrast two unlike sign BPS particles may be thought of as colliding objects moving in opposite directions in compact space. This leads to complicated interactions which are totally intractable at present. We illustrate this by considering the potential between opposite sign zero-D- branes .

hep-th↗
arXiv1995

The Number of States of Two Dimensional Critical String Theory

We discuss string theory vacua which have the wrong number of spacetime dimensions, and give a crude argument that vacua with more than four large dimensions are improbable. We then turn to two dimensional vacua, which naively appear to violate Bekenstein's entropy principle. A classical analysis shows that the naive perturbative counting of states is unjustified. All excited states of the system have strong coupling singularities which prevent us from concluding that they really exist. A speculative interpretation of the classical solutions suggests only a finite number of states will be found in regions bounded by a finite area. We also argue that the vacuum degeneracy of two dimensional classical string theory is removed in quantum mechanics. The system appears to be in a Kosterlitz-Thouless phase. This leads to the conclusion that it is also improbable to have only two large spacetime dimensions in string theory. However, we note that, unlike our argument for high dimensions, our conclusions about the ground state have neglected two dimensional quantum gravitational effects, and are at best incomplete.

hep-th↗