Related papers: $SO(4)$ Landau Models and Matrix Geometry

We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than 4 dimensions, a SU(n) gauge theory on a Moyal-Weyl space arises with…

We examine the $5d$ Yang-Mills matrix model in $0+1$-dimensions with $U(4N)$ gauge symmetry and a mass deformation term. We determine the explicit $SU(4)\approx SO(6)$ equivariant parametrizations of the gauge field and the fluctuations…

We study non-linear electrodynamics in curved space from the viewpoint of dualities. After establishing the existence of a topological bound for self-dual configurations of Born-Infeld field in curved space, we check that the…

We explore the hyperbolic geometry of squeezed states in the perspective of the non-compact Hopf map. Based on analogies between squeeze operation and $Sp(2,\mathbb{R})$ hyperbolic rotation, two types of the squeeze operators, the (usual)…

We numerically study the SU(2) gauge theory with two dynamical flavors of the domain-wall fermions in fundamental representation. The meson spectra and the residual mass are measured on three lattice volumes and at two values of gauge…

We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy $S^{4}$ appears naturally in this theory. The fuzzy monopole…

We construct the complete and explicit non-linear Kaluza-Klein Ansatz for deriving the bosonic sector of the standard N=4 SO(4) gauged four-dimensional supergravity from the reduction of D=11 supergravity on S^7. This provides a way of…

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum,…

The three-dimensional complexified exteriour bundle $C \otimes \Lambda(R^3)$ is proposed as a geometric interpretation of electroweak doublets of Dirac fermions. The Dirac equation on this bundle allows a staggered discretization on a…

We show the existence and uniqueness of a massless supersymmetric ground state wavefunction of a SU(2) matrix model in a bounded smooth domain with Dirichlet boundary conditions. This is a gauge system and we provide a new framework to…

We present the first formulation of linearised gravity in four dimensions which is manifestly Lorentz covariant and democratic, i.e. treats the two frames related by electric-magnetic duality on equal footing. It is well-known that…

We report on the status of our programme to simulate Sp($2N$) gauge theories on the lattice. Motivated by the potential realization of an SU($4$)/Sp($4$)$\sim$SO($6$)/SO($5$) composite Higgs model and the applications to self interacting…

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…

We study certain new models of supersymmetric quantum mechanics. The explicit form of the corresponding superfield and component actions, as well as of the quantum Hamiltonians and supercharges is given. It is shown that the Hamiltonian…

We show that the classical equations of motion for a particle on three dimensional fuzzy space and on the fuzzy sphere are underpinned by a natural Lorentz geometry. From this geometric perspective, the equations of motion generally…

Motivated by the spin from isospin mechanism of Jackiw-Rebbi-Hasenfratz-'t Hooft, we study two SU(2) gauged supergravity solutions of the form $M_{d}\times\text{S}^{2}$ containing non-Abelian hedgehog monopole on the 2-sphere. Due to the…

Liouville and Toda gravity theories with non-vanishing interaction potentials have spectra obtained by dividing the free-field spectra for these cases by the Weyl group of the corresponding $A_1$ or $A_2$ Lie algebra. We study the canonical…

Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using…

This work is the second installment of a series on the loop-string-hadron (LSH) approach to SU(3) lattice Yang-Mills theory. Here, we present the infinite-dimensional matrix representation for arbitrary gauge-invariant operators at a…

The $N=4$ SU(2)$_k$ superconformal algebra has the global automorphism of SO(4) $\approx$ SU(2)$\times$SU(2) with the {\it left} factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by…