相关论文: Master Field on Fuzzy Sphere
We discuss the squashed fuzzy sphere, which is a projection of the fuzzy sphere onto the equatorial plane, and use it to illustrate the stringy aspects of noncommutative field theory. We elaborate explicitly how strings linking its two…
We study and analyse the questions regarding breakdown of global symmetry on noncommutative sphere. We demonstrate this by considering a complex scalar field on a fuzzy sphere and isolating Goldstone modes. We discuss the role of nonlocal…
It is generally believed that the space has a nontrivial structure which is apparent on the order of the Planck length. There is a class of models of three-dimensional quantum spaces constructed using different mathematical tools. Also,…
We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…
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…
The basic concepts of non-commutative probability theory are reviewed and applied to the large $N$ limit of matrix models. We argue that this is the appropriate framework for constructing the master field in terms of which large $N$…
The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined. The local U(1) gauge transformation on the fuzzy sphere is…
Boundary conformal field theory (BCFT) provides a universal framework for critical phenomena in the presence of boundaries. We determine BCFT data for the normal and ordinary boundary universality classes of the $1+1$-dimensional boundaries…
The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These…
Using the concept of fuzzy field, we have considered the fuzzy field of real and complex numbers and thereafter we have established a few standard results of real and complex numbers with respect to a membership function.
In spacetime dimensions larger than 2, whenever a global symmetry G is spontaneously broken to a subgroup H, and G and H are Lie groups, there are Nambu-Goldstone modes described by fields with values in G/H. In two-dimensional spacetimes…
The master fields for the large $N$ limit of matrix models and gauge theory are constructed. The master fields satisfy to standard equations of relativistic field theory but fields are quantized according to a new rule. To define the master…
This is a short review of recent work on fuzzy spaces in their relation to the M(atrix) theory and the quantum Hall effect. We give an introduction to fuzzy spaces and how the limit of large matrices is obtained. The complex projective…
We study the phase diagram of the scalar field theory on the fuzzy sphere described as a particular multitrace matrix model. We consider perturbative and nonperturbative terms in the kinetic term effective action and describe consequences…
A relationship between real, complex, and quaternionic vector fields on spheres is given by using a relationship between the corresponding standard inner products. The number of linearly independent complex vector fields on the standard…
We study the spontaneous symmetry breaking of O(3) scalar field on a fuzzy sphere $S_F^2$. We find that the fluctuations in the background of topological configurations are finite. This is in contrast to the fluctuations around a uniform…
In this paper, we consider the geometrical quantities on the fuzzy sphere from the spectral point of view, such as the area and the dimension. We find that, in contract to the standard sphere, the area and the dimension are the functions of…
We formulate theory of interacting scalar field on the fuzzy sphere as a random matrix model. We then analyze the expectation values of observables of the theory in the large N limit and we demonstrate that the eigenvalue distribution of…
A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly…
We present an analysis of two different approximations to the scalar field theory on the fuzzy sphere, a nonperturbative and a perturbative one, which are both multitrace matrix models. We show that the former reproduces a phase diagram…