Related papers: $SO(4)$ Landau Models and Matrix Geometry
The sO(3) and the Lorentz algebra symmetries breaking with gauge curvatures are studied by means of a covariant Hamiltonian. The restoration of these algebra symmetries in flat and curved spaces is performed and led to the apparition of a…
Landau levels (LLs) are of great importance for understanding the quantum Hall effect and associated many-body physics. Recently, their three-dimensional (3D) counterparts, i.e., dispersionless 3D LLs with well-defined quantum numbers, have…
We theoretically investigate three-dimensional singular flat band systems, focusing on their quantum geometric properties and response to external magnetic fields. As a representative example, we study the pyrochlore lattice, which hosts a…
Here we have illustrated the construction of a real structure on fuzzy sphere $S^2_*$ in its spin-1/2 representation. Considering the SU(2) covariant Dirac and chirality operator on $S^2_*$ given by Watamura et. al. in [6], we have shown…
We formulate the $O(3) \s-$ model on fuzzy sphere and construct the Hopf term. We show that the field can be expanded in terms of the ladder operators of Holstein-Primakoff realisation of SU(2) algebra and the corresponding basis set can be…
We propose gauge parameterization of the three-dimensional $n$-field using orthogonal SO(3)-matrix which, in turn, is defined by a field taking values in the Lie algebra so(3) (rotational-angle field). The rotational-angle field has an…
We start with an $SU(\cal {N})$ Yang-Mills theory on a manifold ${\cal M}$, suitably coupled to two distinct set of scalar fields in the adjoint representation of $SU({\cal N})$, which are forming a doublet and a triplet, respectively under…
Configurations of pure SU(2) gauge field theory on the lattice are transformed to Landau gauge. After Fourier transformation, large momentum amplitudes are suppressed (filtered) by a variable amount, and the configurations are transformed…
Based on the generalized valence bond picture, a Schwinger boson mean field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in…
Following Henyey procedure, we construct examples of zero modes of the Faddev-Popov operator in the Landau gauge in Euclidean space in D dimensions, for both SU(2) and SU(3 groups. We consider gauge field configurations $A^a_\mu$ which give…
We present a study of D=4 supersymmetric Yang-Mills matrix models with SO(3) mass terms based on the cohomological approach and the Monte Carlo method. In the bosonic models we show the existence of an exotic first/second order transition…
In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital…
We formulate a model of noncommutative four-dimensional gravity on a covariant fuzzy space based on SO(1,4), that is the fuzzy version of the $\text{dS}_4$. The latter requires the employment of a wider symmetry group, the SO(1,5), for…
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…
We consider the $SO(4,1)$-covariant fuzzy hyperboloid $H^4_n$ as a solution of Yang-Mills matrix models, and study the resulting higher-spin gauge theory. The degrees of freedom can be identified with functions on classical $H^4$ taking…
In this paper we investigate the consequences of imposing an SO(4) symmetry both on the scalar field and on spacetime prior to any spontaneous symmetry breakdown in the electroweak model. First we argue that the local electroweak gauge…
We present the first example of super Landau model with both N=4 worldline supersymmetry and non-trivial target space supersymmetry ISU(2|2). The model also reveals a hidden second N=4 supersymmetry which, together with the manifest one,…
We construct a Dirac operator on the quantum sphere $S^2_q$ which is covariant under the action of $SU_q(2)$. It reduces to Watamuras' Dirac operator on the fuzzy sphere when $q\to 1$. We argue that our Dirac operator may be useful in…
Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra,…
The pseudo-SU(3) model is extended to explicitly include the spin and proton-neutron degrees of freedom. A general formalism for evaluating matrix elements of one-body and two-body tensor operators within this framework is presented. The…