Related papers: On Higher Dimensional Fuzzy Spherical Branes
Matrix descriptions of even dimensional fuzzy spherical branes $S^{2k} $ in Matrix Theory and other contexts in Type II superstring theory reveal, in the large $N$ limit, higher dimensional geometries $SO(2k+1)/U(k)$, which have an…
We study $SO(m)$ covariant Matrix realizations of $ \sum_{i=1}^{m} X_i^2 = 1 $ for even $m$ as candidate fuzzy odd spheres following hep-th/0101001. As for the fuzzy four sphere, these Matrix algebras contain more degrees of freedom than…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
We study in detail generalized 4-dimensional fuzzy spheres with twisted extra dimensions. These spheres can be viewed as $SO(5)$-equivariant projections of quantized coadjoint orbits of $SO(6)$. We show that they arise as solutions in…
These notes are a short review of the q-deformed fuzzy sphere S^2_{q,N}, which is a ``finite'' noncommutative 2-sphere covariant under the quantum group U_q(su(2)). We discuss its real structure, differential calculus and integration for…
In matrix models, higher dimensional D-branes are obtained by imposing a noncommutative relation to coordinates of lower dimensional D-branes. On the other hand, a dual description of this noncommutative space is provided by higher…
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…
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,…
Fuzzy spaces like the fuzzy sphere or the fuzzy torus have received remarkable attention, since they appeared as objects in string theory. Although there are many higher dimensional examples, the most known and most studied fuzzy spaces are…
We introduce the fuzzy supersphere as sequence of finite-dimensional, noncommutative $Z_{2}$-graded algebras tending in a suitable limit to a dense subalgebra of the $Z_{2}$-graded algebra of ${\cal H}^{\infty}$-functions on the $(2|…
The symmetry preserving D-branes in coset theories have previously been described as being centered around projections of products of conjugacy classes in the underlying Lie groups. Here, we investigate the coset where a diagonal action of…
A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These…
Using a D0-brane as a probe, we study the spacetime geometry in the neighborhood of N D-branes in matrix theory. We find that due to fermionic zero modes, the coordinates of the probe in the transverse directions are noncommutative, and the…
Coset models and their symmetry preserving branes are studied from a representation theoretic perspective, relating e.g. the horizontal branching spaces to a truncation of the space of bulk fields, and accounting for field identification.…
We consider space and time dependent fuzzy spheres $S^{2p}$ arising in $D1-D(2p+1)$ intersections in IIB string theory and collapsing D(2p)-branes in IIA string theory. In the case of $S^2$, where the periodic space and time-dependent…
The fuzzy sphere, as a quantum metric space, carries a sequence of metrics which we describe in detail. We show that the Bloch coherent states, with these spectral distances, form a sequence of metric spaces that converge to the round…
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…
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined…
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…
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…