Related papers: CP^n Model on Fuzzy Sphere
We study the bosonic and fermionic zero modes in noncommutative instanton backgrounds based on the ADHM construction. In k instanton background in U(N) gauge theory, we show how to explicitly construct 4Nk (2Nk) bosonic (fermionic) zero…
Boundaries not only are fundamental elements in nearly all realistic physical systems, but also greatly enrich the structure of quantum field theories. In this paper, we demonstrate that conformal field theory (CFT) with a boundary, known…
We introduce a simple model to realize the free real scalar CFT on the fuzzy sphere. The model is structurally similar to the original model that realizes the 3D Ising CFT on the fuzzy sphere. Owing to the shift symmetry of the free scalar,…
We fix the long-standing ambiguity in the 1-loop contribution to the mass of a 1+1-dimensional supersymmetric soliton by adopting a set of boundary conditions which follow from the symmetries of the action and which depend only on the…
Fuzzy spheres appear as classical solutions in a matrix model obtained via dimensional reduction of 3-dimensional Yang-Mills theory with the Chern-Simons term. Well-defined perturbative expansion around these solutions can be formulated…
The Atiyah-Singer index theorem on a closed manifold is well understood and appreciated in physics. On the other hand, the Atiyah-Patodi-Singer index, which is an extension to a manifold with boundary, is physicist-unfriendly, in that it is…
In the previous papers, we studied the 't Hooft-Polyakov (TP) monopole configurations in the U(2) gauge theory on the fuzzy 2-sphere,and showed that they have nonzero topological charge in the formalism based on the Ginsparg-Wilson (GW)…
The scattering of fermions in the background field of a topological soliton of the modified $(2 + 1)$-dimensional $\mathbb{CP}^{1}$ model is studied here both analytically and numerically. Unlike the original $\mathbb{CP}^{1}$ model, the…
Recently introduced ''fuzzy sphere'' method has enabled accurate numerical regularizations of certain three-dimensional (3D) conformal field theories (CFTs). The regularization is provided by the non-commutative geometry of the lowest…
We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is…
We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in ${\cal N}=2$ supersymmetric Abelian gauge theories in four dimensions. We obtain solutions to the 1/4 BPS equations with the…
We study the domain wall soliton solutions in the relativistic self-dual Maxwell Chern-Simons model in 1+1 dimensions obtained by the dimensional reduction of the 2+1 model. Both topological and nontopological self-dual solutions are found…
Four-dimensional manifolds with changing signature are obtained by taking the large $N$ limit of fuzzy $CP^2$ solutions to a Lorentzian matrix model. The regions of Lorentzian signature give toy models of closed universes which exhibit…
We determine the Chern characters of two projective modules over the fuzzy sphere and calculate the corresponding topological charges (Chern numbers). These turn out to have corrections - compared to the commutative limit - induced by the…
We demonstrate that in the supersymmetric extensions of a class of generalized (or K) field theories introduced recently, the static energy satisfies a BPS bound in each topological sector. Further, the corresponding soliton solutions…
We study polynomial deformations of the fuzzy sphere, specifically given by the cubic or the Higgs algebra. We derive the Higgs algebra by quantizing the Poisson structure on a surface in $\mathbb{R}^3$. We find that several surfaces,…
We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a…
The quantum Hall effect is studied in a spherical geometry using the Dirac operator for non-interacting fermions in a background magnetic field, which is supplied by a Wu-Yang magnetic monopole at the centre of the sphere. Wave functions…
We consider the physics of a matrix model describing D0-brane dynamics in the presence of an RR flux background. Non-commuting spaces arise as generic soltions to this matrix model, among which fuzzy spheres have been studied extensively as…
We use the non-Abelian DBI action to study the dynamics of $N$ coincident $Dp$-branes in an arbitrary curved background, with the presence of a homogenous world-volume electric field. The solutions are natural extensions of those without…