Related papers: Lorentzian Fuzzy Spheres
Free theories are landmarks in the landscape of quantum field theories: their exact solvability serves as a pillar for perturbative constructions of interacting theories. Fuzzy sphere regularization, which combines quantum Hall physics with…
We explore a new way to simulate quantum field theory, without introducing a spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4 model. The regularisation consists of a fuzzy sphere with radius R for the two…
We present a numerical study of a two dimensional model of the Wess-Zumino type. We formulate this model on a sphere, where the fields are expanded in spherical harmonics. The sphere becomes fuzzy by a truncation in the angular momenta.…
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 fuzzy-sphere regularisation is a powerful tool to study conformal field theories (CFT) in three spacetime dimensions. In this paper, we extend its scope to CFTs with local fermionic operators. We realise the free-Majorana-fermion CFT on…
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…
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…
The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $\varphi^4$ scalar field theory on it and analyze numerically for…
We construct various exact analytical solutions of the $SO(3)$ BMN matrix model that correspond to rotating fuzzy spheres and rotating fuzzy tori.These are also solutions of Yang Mills theory compactified on a sphere times time and they are…
Recently we have introduced a matrix model depending on two coupling constants $g^2$ and $\lambda$, which contains the fuzzy sphere as a background; to obtain the classical limit $g^2$ must depend on $N$ in a precise way. In this paper we…
We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian…
The fuzzy sphere method has enjoyed great success in the study of (2+1)-dimensional unitary conformal field theories (CFTs) by regularizing them as quantum Hall transitions on the sphere. Here, we extend this approach to the Yang-Lee…
We study perturbations of 4-dimensional fuzzy spheres as backgrounds in the IKKT or IIB matrix model. Gauge fields and metric fluctuations are identified among the excitation modes with lowest spin, supplemented by a tower of higher-spin…
We consider general $k=-1$ FLRW covariant quantum spacetimes $\mathcal{M}^{3,1} \times \mathcal{K}$ with fuzzy extra dimensions $\mathcal{K}$ as classical solutions of the IKKT matrix model. The coupled equations of motion are recast in…
A fuzzy circle and a fuzzy 3-sphere are constructed as subspaces of fuzzy complex projective spaces, of complex dimension one and three, by modifying the Laplacians on the latter so as to give unwanted states large eigenvalues. This leaves…
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…
The phi^4 real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a disordered phase, and a non-uniform ordered…
The Lorentzian Hamiltonian constraint is solved for isotropic loop quantum cosmology coupled to a massless scalar field. As in the Euclidean case, the discreteness of quantum geometry removes the classical singularity from the quantum…
We study the fate of the fuzzy sphere vacuum solutions in the SU(N)xSU(N+M) Klebanov-Strassler theory at finite temperature and at weak coupling. We find that thermal effects push the S^2 radius --a modulus at T=0-- towards vanishing size.…
We present a new type of matrix regularization, which is based on matrix-valued functions defined on a cylinder. If non-commutative coordinates of a fuzzy space are defined by a regularization of such functions, we show that a classical…