1,638 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
The Structure of Spacetime and Noncommutative Geometry
We give a general and nontechnical review of some aspects of noncommutative
geometry as a tool to understand the structure of spacetime. We discuss the
motivations for the constructions of a noncommutative geometry, and the passage
from commutative to noncommutative spaces. We then give a brief description of
Connes approach to the standard model, of the noncommutative geometry of
strings and of field theory on noncommutative spaces. We also discuss the role
of symmetries and some possible consequences for cosmology.Comment: 30 pages, Talk given at the workshop: Geometry, Topology, QFT and
Cosmology, Paris, 28-30 May 2008. To appear in the proceeding
Points. Lack thereof
I will discuss some aspects of the concept of "point" in quantum gravity,
using mainly the tool of noncommutative geometry. I will argue that at Planck's
distances the very concept of point may lose its meaning. I will then show how,
using the spectral action and a high momenta expansion, the connections between
points, as probed by boson propagators, vanish. This discussion follows closely
[1] (Kurkov-Lizzi-Vassilevich Phys. Lett. B 731 (2014) 311, [arXiv:1312.2235
[hep-th]].Comment: Proceedings of the XXII Krakow Methodological Conference: Emergence
of the Classical, Copernicus Centre, 11-12 October 2018. Mostly based on
arXiv:1312.2235. V2 corrects several typo
Strings, Noncommutative Geometry and the Size of the Target Space
We describe how the presence of the antisymmetric tensor (torsion) on the
world sheet action of string theory renders the size of the target space a
gauge non invariant quantity. This generalizes the R 1/R symmetry in which
momenta and windings are exchanged, to the whole O(d,d,Z). The crucial point is
that, with a transformation, it is possible always to have all of the lowest
eigenvalues of the Hamiltonian to be momentum modes. We interpret this in the
framework of noncommutative geometry, in which algebras take the place of point
spaces, and of the spectral action principle for which the eigenvalues of the
Dirac operator are the fundamental objects, out of which the theory is
constructed. A quantum observer, in the presence of many low energy eigenvalues
of the Dirac operator (and hence of the Hamiltonian) will always interpreted
the target space of the string theory as effectively uncompactified.Comment: 19 pages, LateX, instructions for older LateX version
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
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
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
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
Dimensional Deception from Noncommutative Tori: An alternative to Horava-Lifschitz
We study the dimensional aspect of the geometry of quantum spaces.
Introducing a physically motivated notion of the scaling dimension, we study in
detail the model based on a fuzzy torus. We show that for a natural choice of a
deformed Laplace operator, this model demonstrates quite non-trivial behaviour:
the scaling dimension flows from 2 in IR to 1 in UV. Unlike another model with
the similar property, the so-called Horava-Lifshitz model, our construction
does not have any preferred direction. The dimension flow is rather achieved by
a rearrangement of the degrees of freedom. In this respect the number of
dimensions is deceptive. Some physical consequences are discussed.Comment: 20 pages + extensive appendix. 3 figure
Matrix Bases for Star Products: a Review
We review the matrix bases for a family of noncommutative products
based on a Weyl map. These products include the Moyal product, as well as the
Wick-Voros products and other translation invariant ones. We also review the
derivation of Lie algebra type star products, with adapted matrix bases. We
discuss the uses of these matrix bases for field theory, fuzzy spaces and
emergent gravity
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