411 research outputs found
Hidden classical symmetry in quantum spaces at roots of unity : From q-sphere to fuzzy sphere
19 pages in harvmac big, 5 figures; v2: refs added ; v3: more refs added19 pages in harvmac big, 5 figures; v2: refs added ; v3: more refs added19 pages in harvmac big, 5 figures; v2: refs added ; v3: more refs addedWe study relations between different kinds of non-commutative spheres which have appeared in the context of ADS/CFT correspondences recently, emphasizing the connections between spaces that have manifest quantum group symmetry and spaces that have manifest classical symmetry. In particular we consider the quotient at roots of unity, and find its relations with the fuzzy sphere with manifest classical SU(2) symmetry. Deformation maps between classical and quantum symmetry, the module structure of quantum spheres and the structure of indecomposable representations of at roots of unity conspire in an interesting way to allow the relation between manifestly symmetric spheres and manifestly U(SU(2)) symmetric spheres. The relation suggests that a subset of field theory actions on the q-sphere are equivalent to actions on the fuzzy sphere. The results here are compatible with the proposal that quantum spheres at roots of unity appear as effective geometries which account for finite N effects in the ADS/CFT correspondence
Evaluation Of Glueball Masses From Supergravity
In the framework of the conjectured duality relation between large gauge
theory and supergravity the spectra of masses in large gauge theory can be
determined by solving certain eigenvalue problems in supergravity. In this
paper we study the eigenmass problem given by Witten as a possible
approximation for masses in QCD without supersymmetry. We place a particular
emphasis on the treatment of the horizon and related boundary conditions. We
construct exact expressions for the analytic expansions of the wave functions
both at the horizon and at infinity and show that requiring smoothness at the
horizon and normalizability gives a well defined eigenvalue problem. We show
for example that there are no smooth solutions with vanishing derivative at the
horizon. The mass eigenvalues up to corresponding to smooth
normalizable wave functions are presented. We comment on the relation of our
work with the results found in a recent paper by Cs\'aki et al.,
hep-th/9806021, which addresses the same problem.Comment: 20 pages,Latex,3 figs,psfig.tex, added refs., minor change
Seiberg-Witten Transforms of Noncommutative Solitons
We evaluate the Seiberg-Witten map for solitons and instantons in
noncommutative gauge theories in various dimensions. We show that solitons
constructed using the projection operators have delta-function supports when
expressed in the commutative variables. This gives a precise identification of
the moduli of these solutions as locations of branes. On the other hand, an
instanton solution in four dimensions allows deformation away from the
projection operator construction. We evaluate the Seiberg-Witten transform of
the U(2) instanton and show that it has a finite size determined by the
noncommutative scale and by the deformation parameter \rho. For large \rho, the
profile of the D0-brane density of the instanton agrees surprisingly well with
that of the BPST instanton on commutative space.Comment: 29 pages, LaTeX; comments added, typos corrected, and a reference
added; comments added, typos correcte
Intersecting D-branes in Type IIB Plane Wave Background
We study intersecting D-branes in a type IIB plane wave background using
Green-Schwarz worldsheet formulation. We consider all possible -branes
intersecting at angles in the plane wave background and identify their residual
supersymmetries. We find, in particular, that brane
intersections preserve no supersymmetry. We also present the explicit
worldsheet expressions of conserved supercharges and their supersymmetry
algebras.Comment: 32 pages, 2 tables; Corrected typos, to appear in Phys. Rev.
Can Quantum de Sitter Space Have Finite Entropy?
If one tries to view de Sitter as a true (as opposed to a meta-stable)
vacuum, there is a tension between the finiteness of its entropy and the
infinite-dimensionality of its Hilbert space. We invetsigate the viability of
one proposal to reconcile this tension using -deformation. After defining a
differential geometry on the quantum de Sitter space, we try to constrain the
value of the deformation parameter by imposing the condition that in the
undeformed limit, we want the real form of the (inherently complex) quantum
group to reduce to the usual SO(4,1) of de Sitter. We find that this forces
to be a real number. Since it is known that quantum groups have
finite-dimensional representations only for root of unity, this suggests
that standard -deformations cannot give rise to finite dimensional Hilbert
spaces, ruling out finite entropy for q-deformed de Sitter.Comment: 10 pages, v2: references added, v3: minor corrections, abstract and
title made more in-line with the result, v4: published versio
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