58 research outputs found
Fuzzy Conifold and Monopoles on
In this article, we construct the fuzzy (finite dimensional) analogues of the
conifold and its base . We show that fuzzy is (the analogue
of) a principal U(1) bundle over fuzzy spheres and
explicitly construct the associated monopole bundles. In particular our
construction provides an explicit discretization of the spaces
and
Monopoles On From The Fuzzy Conifold
The intersection of the conifold and is a
compact 3--dimensional manifold . We review the description of as a
principal U(1) bundle over and construct the associated monopole line
bundles. These monopoles can have only even integers as their charge. We also
show the Kaluza--Klein reduction of to provides an easy
construction of these monopoles. Using the analogue of the Jordon-Schwinger
map, our techniques are readily adapted to give the fuzzy version of the
fibration and the associated line bundles. This is an
alternative new realization of the fuzzy sphere and monopoles on it.Comment: version submitted to JHE
Fuzzy Cosets and their Gravity Duals
Dp-branes placed in a certain external RR (p+4)-form field expand into a
transverse fuzzy two-sphere, as shown by Myers. We find that by changing the
(p+4)-form background other fuzzy cosets can be obtained. Three new examples,
S^2 X S^2, CP^2 and SU(3)/(U(1) X U(1)) are constructed. The first two are
four-dimensional while the last is six-dimensional. The dipole and quadrupole
moments which result in these configurations are discussed. Finally, the
gravity backgrounds dual to these vacua are examined in a leading order
approximation. These are multi-centered solutions containing (p+4)- or
(p+6)-dimensional brane singularities.Comment: 36 pages, harvmac, no figures, two references adde
Twisted Conformal Symmetry in Noncommutative Two-Dimensional Quantum Field Theory
By twisting the commutation relations between creation and annihilation
operators, we show that quantum conformal invariance can be implemented in the
2-d Moyal plane. This is an explicit realization of an infinite dimensional
symmetry as a quantum algebra.Comment: 10 pages. Text enlarged. References adde
Quantum Entropy for the Fuzzy Sphere and its Monopoles
Using generalized bosons, we construct the fuzzy sphere and monopoles
on in a reducible representation of . The corresponding quantum
states are naturally obtained using the GNS-construction. We show that there is
an emergent non-abelian unitary gauge symmetry which is in the commutant of the
algebra of observables. The quantum states are necessarily mixed and have
non-vanishing von Neumann entropy, which increases monotonically under a
bistochastic Markov map. The maximum value of the entropy has a simple relation
to the degeneracy of the irreps that constitute the reducible representation
that underlies the fuzzy sphere.Comment: 21 pages, typos correcte
A Matrix Model for QCD: QCD Colour is Mixed
We use general arguments to show that coloured QCD states when restricted to
gauge invariant local observables are mixed. This result has important
implications for confinement: a pure colourless state can never evolve into two
coloured states by unitary evolution. Furthermore, the mean energy in such a
mixed coloured state is infinite. Our arguments are confirmed in a matrix model
for QCD that we have developed using the work of Narasimhan and Ramadas and
Singer. This model, a -dimensional quantum mechanical model for gluons
free of divergences and capturing important topological aspects of QCD, is
adapted to analytical and numerical work. It is also suitable to work on large
QCD. As applications, we show that the gluon spectrum is gapped and also
estimate some low-lying levels for and 3 (colors).
Incidentally the considerations here are generic and apply to any non-abelian
gauge theory.Comment: 16 pages, 3 figures. V2: comments regarding infinite energy and
confinement adde
Thermal Correlation Functions of Twisted Quantum Fields
We derive the thermal correlators for twisted quantum fields on
noncommutative spacetime. We show that the thermal expectation value of the
number operator is same as in commutative spacetime, but that higher
correlators are sensitive to the noncommutativity parameters .Comment: 4 pages, LaTeX. Reference added, typos corrected
Aspects of Boundary Conditions for Nonabelian Gauge Theories
The boundary values of the time-component of the gauge potential form
externally specifiable data characterizing a gauge theory. We point out some
consequences such as reduced symmetries, bulk currents for manifolds with
disjoint boundaries and some nuances of how the charge algebra is realized.Comment: 15 page
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