9,649 research outputs found
Matrix models on the fuzzy sphere
Field theory on a fuzzy noncommutative sphere can be considered as a
particular matrix approximation of field theory on the standard commutative
sphere. We investigate from this point of view the scalar theory. We
demonstrate that the UV/IR mixing problems of this theory are localized to the
tadpole diagrams and can be removed by an appropiate (fuzzy) normal ordering of
the vertex. The perturbative expansion of this theory reduces in the
commutative limit to that on the commutative sphere.Comment: 6 pages, LaTeX2e, Talk given at the NATO Advanced Research Workshop
on Confiment, Topology, and other Non-Perturbative Aspects of QCD, Stara
Lesna, Slovakia, Jan. 21-27, 200
Topologically nontrivial field configurations in noncommutative geometry
In the framework of noncommutative geometry we describe spinor fields with
nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding
field theory actions conserve all basic symmetries of the standard commutative
version (space isometries and global chiral symmetry), but due to the
noncommutativity of the space the fields are regularized and they contain only
finite number of modes.Comment: 27 pages, LaTeX (normalization coefficients in Eqs. (93) corrected
Simple field theoretical models on noncommutative manifolds
We review recent progress in formulating two-dimensional models over
noncommutative manifolds where the space-time coordinates enter in the
formalism as non-commuting matrices. We describe the Fuzzy sphere and a way to
approximate topological nontrivial configurations using matrix models. We
obtain an ultraviolet cut off procedure, which respects the symmetries of the
model. The treatment of spinors results from a supersymmetric formulation; our
cut off procedure preserves even the supersymmetry.Comment: 15 pages, TeX (based on lectures given by H. Grosse at Workshops in
Clausthal (Germany) and Razlog (Bulgaria) in August 1995
Field Theory on a Supersymmetric Lattice
A lattice-type regularization of the supersymmetric field theories on a
supersphere is constructed by approximating the ring of scalar superfields by
an integer-valued sequence of finite dimensional rings of supermatrices and by
using the differencial calculus of non-commutative geometry. The regulated
theory involves only finite number of degrees of freedom and is manifestly
supersymmetric.Comment: 31 pages, LaTe
Towards Finite Quantum Field Theory in Non-Commutative Geometry
We describe the self-interacting scalar field on the truncated sphere and we
perform the quantization using the functional (path) integral approach. The
theory posseses a full symmetry with respect to the isometries of the sphere.
We explicitely show that the model is finite and the UV-regularization
automatically takes place.Comment: 19 pages, LaTe
Noncommutative QFT and Renormalization
Field theories on deformed spaces suffer from the IR/UV mixing and
renormalization is generically spoiled. In work with R. Wulkenhaar, one of us
realized a way to cure this disease by adding one more marginal operator. We
review these ideas, show the application to models and use the heat
kernel expansion methods for a scalar field theory coupled to an external gauge
field on a -deformed space and derive noncommutative gauge field
actions.Comment: To appear in the proceedings of the Workshop "Noncommutative Geometry
in Field and String Theory", Corfu, 2005 (Greece
Novel Symmetry of Non-Einsteinian Gravity in Two Dimensions
The integrability of -gravity with torsion in two dimensions is traced
to an ultralocal dynamical symmetry of constraints and momenta in Hamiltonian
phase space. It may be interpreted as a quadratically deformed
-algebra with the deformation consisting of the Casimir operators of
the undeformed algebra. The locally conserved quantity encountered in the
explicit solution is identified as an element of the centre of this algebra.
Specific contractions of the algebra are related to specific limits of the
explicit solutions of this model.Comment: 17 pages, TUW-92-04 (LaTeX
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