Related papers: Fuzzy Sphere from Matrix Model
Rotational dynamics is known to polarize D0 branes into higher dimensional fuzzy D$p$-branes: the tension forces between D0 branes provide the centripetal acceleration, and a puffed up spinning configuration stabilizes. In this work, we…
In 5+1 dimensions, we construct a vortex-like solution on a two-dimensional sphere. We study fermionic zero modes in the background of this solution and relate them to the replication of fermion families in the Standard Model. In…
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 study the interconnection between the finite projective modules for a fuzzy sphere, determined in a previous paper, and the matrix model approach, making clear the physical meaning of noncommutative topological configurations.
The behaviour of matrix string theory in the background of a type IIA pp wave at small string coupling, g_s << 1, is determined by the combination M g_s where M is a dimensionless parameter proportional to the strength of the Ramond-Ramond…
We consider the dynamics of a charged particle in a space whose coordinates are $N\times N$ hermitian matrices. Putting things in the framework of D0-branes of String Theory, we mention that the transformations of the matrix coordinates…
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
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…
We show that fuzzy spheres are solutions of ${\it Lorentzian}$ IKKT matrix models. The fuzzy sphere solutions serve as toy models of closed noncommutative cosmologies where big bang/crunch singularities appear only after taking the…
Following the pattern of the Frobenius structure usually assigned to the 1-dimensional sphere, we investigate the Frobenius structures of spheres in all other dimensions. Starting from dimension $d=1$, all the spheres are commutative…
This thesis is based on hep-th/0203110, hep-th/0005273, hep-th/0107068, hep-th/0106205, and hep-th/0103164, but includes additional results, details, and background material. It covers the description of D-branes on group manifolds based on…
A fuzzy geometry is a certain type of spectral triple whose Dirac operator crucially turns out to be a finite matrix. This notion was introduced in [J. Barrett, J. Math. Phys. 56, 082301 (2015)] and accommodates familiar fuzzy spaces like…
Motivation for the study of spacetime noncommutativity comes primarily from its possible use in investigations of (Planck-scale) spacetime fuzziness, but most work focuses on S-matrix/field-theory observables and still very little has been…
We find an analytical formula for the quasicoherent states of 3D fuzzy spaces defined by algebras generated by bosonic creation and annihilation operators. This one is expressed in a representation onto the coherent states of the CCR…
We consider the noncommutative space $\mathbb{R}^3_\lambda$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a "foliation" of $\mathbb{R}^3$ into fuzzy spheres. We first construct a natural matrix base adapted to…
We use the Myers T-dual nonabelin Born-Infeld action to find some new nontrivial solutions for the branes in the background of D6-branes and Melvin magnetic tube field. In the D6-Branes background we can find both of the fuzzy sphere and…
A detailed Monte Carlo calculation of the phase diagram of bosonic IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are…
In this lecture I review how a matrix/Azumaya-type noncommutative geometry arises for D-branes in string theory and how such a geometry serves as an origin of the master nature of D-branes; and then highlight an abundance conjecture on…
We outline a brief description of non commutative geometry and present some applications in string theory. We use the fuzzy torus as our guiding example.
We investigate the correspondence between the D2-brane, which is described by the abelian Born-Infeld action, and multiple D0-branes, which are done by the nonabelian Born-Infeld action. We construct effective actions for the fuzzy…