Related papers: Covariant 4-dimensional fuzzy spheres, matrix mode…
We examine in detail the higher spin fields which arise on the basic fuzzy sphere $S^4_N$ in the semi-classical limit. The space of functions can be identified with functions on classical $S^4$ taking values in a higher spin algebra…
We examine gauge theories defined in higher dimensions where theextra dimensions form a fuzzy (finite matrix) manifold. First we reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes and then we perform a…
This thesis is devoted to the study of Quantum Field Theories (QFT) on fuzzy spaces. Fuzzy spaces are approximations to the algebra of functions of a continuous space by a finite matrix algebra. In the limit of infinitely large matrices the…
We argue supersymmetric generalizations of fuzzy two- and four-spheres based on the unitary-orthosymplectic algebras, $uosp(N|2)$ and $uosp(N|4)$, respectively. Supersymmetric version of Schwinger construction is applied to derive graded…
We study a noncommutative gauge theory on a fuzzy four-sphere. The idea is to use a matrix model with a fifth-rank Chern-Simons term and to expand matrices around the fuzzy four-sphere which corresponds to a classical solution of this…
The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three…
Whereas the classical sphere $C P^1$ can be defined as the coordinate algebra generated by the matrix entries of a projector $e$ with $\trace(e)=1$, the fuzzy-sphere is defined in the same way by $\trace(e)=1+\lambda$. We show that the…
We include fermions to the model proposed in hep-th/0606021, and obtain a renormalizable 4-dimensional SU(N) gauge theory which spontaneously generates fuzzy extra dimensions and behaves like Yang-Mills theory on M^4 \times S^2. We find a…
We construct a fuzzy $S^4$, utilizing the fact that ${\bf CP}^3$ is an $S^2$ bundle over $S^4$. We find that a fuzzy $S^4$ can be described by a block-diagonal form whose embedding square matrix represents a fuzzy ${\bf CP}^3$. We discuss…
Guided by ordinary quantum mechanics we introduce new fuzzy spheres of dimensions d=1,2: we consider an ordinary quantum particle in D=d+1 dimensions subject to a rotation invariant potential well V(r) with a very sharp minimum on a sphere…
The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is…
In plane-wave matrix model, the membrane fuzzy sphere extended in the SO(3) symmetric space is allowed to have periodic motion on a sub-plane in the SO(6) symmetric space. We consider a background configuration composed of two such fuzzy…
We present a renormalizable 4-dimensional SU(N) gauge theory with a suitable multiplet of scalar fields, which dynamically develops extra dimensions in the form of a fuzzy sphere S^2. We explicitly find the tower of massive Kaluza-Klein…
In the present contribution the construction of particle physics models in theories with fuzzy extra dimensions is discussed. We focus on a bottom-up approach where the structure of a higher-dimensional theory arises within ordinary…
The fuzzy algebra of S^4 is discussed by quantum deformation. To this end we embed the classical S^4 in the Kaehler coset space SO(5)/U(2). The harmonic functions of S^4 are constructed in terms of the complex coordinates of SO(5)/U(2).…
The phenomena of emergent fuzzy geometry and noncommutative gauge theory from Yang-Mills matrix models is briefly reviewed. In particular, the eigenvalues distributions of Yang-Mills matrix models in lower dimensions in the commuting…
We briefly report our recent construction of new fuzzy spheres of dimensions d=1,2 covariant under the full orthogonal group O(D), D=d+1. They are built by imposing a suitable energy cutoff on a quantum particle in D dimensions subject to a…
A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy…
We study the size and shape statistics of ground state fuzzy spheres when projected onto the transverse plane, utilizing the regularized SU(N=2) matrix model in D=(1+3)-dimensional spacetime. We show that they appear as ellipses, from…
Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S^2 and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field…