24,123 research outputs found
Decoding the matrix: Coincident membranes on the plane wave
At the core of nonperturbative theories of quantum gravity lies the
holographic encoding of bulk data in large matrices. At present this mapping is
poorly understood. The plane wave matrix model provides a laboratory for
isolating aspects of this problem in a controlled setting.
At large boosts, configurations of concentric membranes become superselection
sectors, whose exact spectra are known. From the bulk point of view one expects
product states of individual membranes to be contained within the full
spectrum. However, for non-BPS states this inclusion relation is obscured by
Gauss law constraints. Its validity rests on nontrivial relations in
representation theory, which we identify and verify by explicit computation.Comment: 43 pages, 2 figure
Quantum models of classical mechanics: maximum entropy packets
In a previous paper, a project of constructing quantum models of classical
properties has been started. The present paper concludes the project by turning
to classical mechanics. The quantum states that maximize entropy for given
averages and variances of coordinates and momenta are called ME packets. They
generalize the Gaussian wave packets. A non-trivial extension of the
partition-function method of probability calculus to quantum mechanics is
given. Non-commutativity of quantum variables limits its usefulness. Still, the
general form of the state operators of ME packets is obtained with its help.
The diagonal representation of the operators is found. A general way of
calculating averages that can replace the partition function method is
described. Classical mechanics is reinterpreted as a statistical theory.
Classical trajectories are replaced by classical ME packets. Quantum states
approximate classical ones if the product of the coordinate and momentum
variances is much larger than Planck constant. Thus, ME packets with large
variances follow their classical counterparts better than Gaussian wave
packets.Comment: 26 pages, no figure. Introduction and the section on classical limit
are extended, new references added. Definitive version accepted by Found.
Phy
Non-Linear Sigma Model on the Fuzzy Supersphere
In this note we develop fuzzy versions of the supersymmetric non-linear sigma
model on the supersphere S^(2,2). In hep-th/0212133 Bott projectors have been
used to obtain the fuzzy CP^1 model. Our approach utilizes the use of
supersymmetric extensions of these projectors. Here we obtain these (super)
-projectors and quantize them in a fashion similar to the one given in
hep-th/0212133. We discuss the interpretation of the resulting model as a
finite dimensional matrix model.Comment: 11 pages, LaTeX, corrected typo
Supersymmetric Quantum Hall Effect on Fuzzy Supersphere
Supersymmetric quantum Hall liquids are constructed on a supersphere in a
supermonopole background. We derive a supersymmetric generalization of the
Laughlin wavefunction, which is a ground state of a hard-core
invariant Hamiltonian. We also present excited topological objects, which are
fractionally charged deficits made by super Hall currents. Several relations
between quantum Hall systems and their supersymmetric extensions are discussed.Comment: Typos corrected, 5 pages, to be published in PR
Giant Gravitons in Conformal Field Theory
Giant gravitons in AdS_5 x S^5, and its orbifolds, have a dual field theory
representation as states created by chiral primary operators. We argue that
these operators are not single-trace operators in the conformal field theory,
but rather are determinants and subdeterminants of scalar fields; the stringy
exclusion principle applies to these operators. Evidence for this
identification comes from three sources: (a) topological considerations in
orbifolds, (b) computation of protected correlators using free field theory and
(c) a Matrix model argument. The last argument applies to AdS_7 x S^4 and the
dual (2,0) theory, where we use algebraic aspects of the fuzzy 4-sphere to
compute the expectation value of a giant graviton operator along the Coulomb
branch of the theory.Comment: 37 pages, LaTeX, 1 figure. v2: references and acknowledgements added,
small correction
- …