462 research outputs found
The Zero Tension Limit of The Virasoro Algebra and the Central Extension
We argue that the Virasoro algebra for the closed bosonic string can be cast
in a form which is suitable for the limit of vanishing string tension. In this
form the limit of the Virasoro algebra gives the null string algebra. The
anomalous central extension is seen to vanish as well when .Comment: LaTeX, 7 pa
Mirror Fermions in Noncommutative Geometry
In a recent paper we pointed out the presence of extra fermionic degrees of
freedom in a chiral gauge theory based on Connes Noncommutative Geometry. Here
we propose a mechanism which provides a high mass to these mirror states, so
that they decouple from low energy physics.Comment: 7 pages, LaTe
From the fuzzy disc to edge currents in Chern-Simons Theory
We present a brief review of the fuzzy disc, the finite algebra approximating
functions on a disc, which we have introduced earlier. We also present a
comparison with recent papers of Balachandran, Gupta and
K\"urk\c{c}\"{u}o\v{g}lu, and of Pinzul and Stern, aimed at the discussion of
edge states of a Chern-Simons theory.Comment: 8 pages, 6 figures, Talk presented at ``Space-time and Fundamental
Interactions: Quantum Aspects'', conference in honour of A. P. Balachandran's
65th birthday. References added and one misprint correcte
Gauge and Poincare' Invariant Regularization and Hopf Symmetries
We consider the regularization of a gauge quantum field theory following a
modification of the Polchinski proof based on the introduction of a cutoff
function. We work with a Poincare' invariant deformation of the ordinary
point-wise product of fields introduced by Ardalan, Arfaei, Ghasemkhani and
Sadooghi, and show that it yields, through a limiting procedure of the cutoff
functions, to a regularized theory, preserving all symmetries at every stage.
The new gauge symmetry yields a new Hopf algebra with deformed co-structures,
which is inequivalent to the standard one.Comment: Revised version. 14 pages. Incorrect statements eliminate
Duality Symmetries and Noncommutative Geometry of String Spacetime
We examine the structure of spacetime symmetries of toroidally compactified
string theory within the framework of noncommutative geometry. Following a
proposal of Frohlich and Gawedzki, we describe the noncommutative string
spacetime using a detailed algebraic construction of the vertex operator
algebra. We show that the spacetime duality and discrete worldsheet symmetries
of the string theory are a consequence of the existence of two independent
Dirac operators, arising from the chiral structure of the conformal field
theory. We demonstrate that these Dirac operators are also responsible for the
emergence of ordinary classical spacetime as a low-energy limit of the string
spacetime, and from this we establish a relationship between T-duality and
changes of spin structure of the target space manifold. We study the
automorphism group of the vertex operator algebra and show that spacetime
duality is naturally a gauge symmetry in this formalism. We show that classical
general covariance also becomes a gauge symmetry of the string spacetime. We
explore some larger symmetries of the algebra in the context of a universal
gauge group for string theory, and connect these symmetry groups with some of
the algebraic structures which arise in the mathematical theory of vertex
operator algebras, such as the Monster group. We also briefly describe how the
classical topology of spacetime is modified by the string theory, and calculate
the cohomology groups of the noncommutative spacetime. A self-contained,
pedagogical introduction to the techniques of noncommmutative geometry is also
included.Comment: 70 pages, Latex, No Figures. Typos and references corrected. Version
to appear in Communications in Mathematical Physic
Matrix Sigma-models for Multi D-brane Dynamics
We describe a dynamical worldsheet origin for the Lagrangian describing the
low-energy dynamics of a system of parallel D-branes. We show how matrix-valued
collective coordinate fields for the D-branes naturally arise as couplings of a
worldsheet sigma-model, and that the quantum dynamics require that these
couplings be mutually noncommutative. We show that the low-energy effective
action for the sigma-model couplings describes the propagation of an open
string in the background of the multiple D-brane configuration, in which all
string interactions between the constituent branes are integrated out and the
genus expansion is taken into account, with a matrix-valued coupling. The
effective field theory is governed by the non-abelian Born-Infeld target space
action which leads to the standard one for D-brane field theory.Comment: 14 pages LaTeX, 1 encapsulated postscript figure; uses epsf.te
String Geometry and the Noncommutative Torus
We construct a new gauge theory on a pair of d-dimensional noncommutative
tori. The latter comes from an intimate relationship between the noncommutative
geometry associated with a lattice vertex operator algebra A and the
noncommutative torus. We show that the (truncated) tachyon subalgebra of A is
naturally isomorphic to a class of twisted modules representing quantum
deformations of the algebra of functions on the torus. We construct the
corresponding even real spectral triples and determine their Morita equivalence
classes using string duality arguments. These constructions yield simple proofs
of the O(d,d;Z) Morita equivalences between -dimensional noncommutative tori
and give a natural physical interpretation of them in terms of the target space
duality group of toroidally compactified string theory. We classify the
automorphisms of the twisted modules and construct the most general gauge
theory which is invariant under the automorphism group. We compute bosonic and
fermionic actions associated with these gauge theories and show that they are
explicitly duality-symmetric. The duality-invariant gauge theory is manifestly
covariant but contains highly non-local interactions. We show that it also
admits a new sort of particle-antiparticle duality which enables the
construction of instanton field configurations in any dimension. The duality
non-symmetric on-shell projection of the field theory is shown to coincide with
the standard non-abelian Yang-Mills gauge theory minimally coupled to massive
Dirac fermion fields.Comment: 37 pages, LaTeX. Major revisions in section 3. Other minor revisions
in the rest of the paper, references adde
Fuzzy de Sitter Space from kappa-Minkowski Space in Matrix Basis
We consider the Lie group generated by the Lie algebra
of -Minkowski space. Imposing the invariance of the metric under the
pull-back of diffeomorphisms induced by right translations in the group, we
show that a unique right invariant metric is associated with
. This metric coincides with the metric of de Sitter
space-time. We analyze the structure of unitary representations of the group
relevant for the realization of the non-commutative
-Minkowski space by embedding into -dimensional Heisenberg
algebra. Using a suitable set of generalized coherent states, we select the
particular Hilbert space and realize the non-commutative -Minkowski
space as an algebra of the Hilbert-Schmidt operators. We define dequantization
map and fuzzy variant of the Laplace-Beltrami operator such that dequantization
map relates fuzzy eigenvectors with the eigenfunctions of the Laplace-Beltrami
operator on the half of de Sitter space-time.Comment: 21 pages, v3 differs from version published in Fortschritte der
Physik by a note and references added and adjuste
Quantum Spacetime, Noncommutative Geometry and Observers
I discuss some issues related to the noncommutative spaces κ and its angular variant ρ-Minkowski with particular emphasis on the role of observers
Dynamical Aspects of Lie--Poisson Structures
Quantum Groups can be constructed by applying the quantization by deformation
procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to
develop an understanding of these structures by investigating dynamical systems
which are associated with this bracket. We look at and , as
submanifolds of a 4--dimensional phase space with constraints, and deal with
two classes of problems. In the first set of examples we consider some
hamiltonian systems associated with Lie-Poisson structures and we investigate
the equations of the motion. In the second set of examples we consider systems
which preserve the chosen bracket, but are dissipative. However in this
approach, they survive the quantization procedure.Comment: 17 pages, figures not include
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