Related papers: 'Schwinger Model' on the Fuzzy Sphere
The q-deformed fuzzy sphere $S_{qF}^2(N)$ is the algebra of $(N+1)\times(N+1)$ dim. matrices, covariant with respect to the adjoint action of $\uq$ and in the limit $q\to 1$, it reduces to the fuzzy sphere $S_{F}^2(N)$. We construct the…
The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere $S^2_F$ can be constructed using the Ginsparg-Wilson(GW) algebra [arxiv:hep-th/0511114]. This construction actually exists for any spin $j$ on $S^2_F$, and have…
We calculate the index of the Dirac operator defined on the q-deformed fuzzy sphere. The index of the Dirac operator is related to its net chiral zero modes and thus to the trace of the chirality operator. We show that for the q-deformed…
The q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $ S^{4}_{qF} $. Using the q-deformed fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed fuzzy Dirac and chirality operators in instanton and…
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…
The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact…
We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the…
It has been constructed the quantum super fuzzy Dirac and chirality operators on q-deformed super fuzzy sphere. Using the quantum super fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed super gauged fuzzy Dirac and chirality…
We construct wave functions and Dirac operator of spin $1/2$ fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly $SO(5)_q$ covariant. We evaluate the engenvalue of…
We consider spinors on the total space of a Kaluza-Klein model with fuzzy sphere fibre and geometrically realised Dirac operator on the product. We show that a single massless spinor on the product appears on spacetime as multiplets of…
We present a manifestly Spin(5) invariant construction of squashed fuzzy $CP^3$ as a fuzzy $S^2$ bundle over fuzzy $S^4$. We develop the necessary projectors and exhibit the squashing in terms of the radii of the $S^2$ and $S^4$. Our…
In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…
We study the second quantization of field theory on the q-deformed fuzzy sphere for real q. This is performed using a path-integral over the modes, which generate a quasiassociative algebra. The resulting models have a manifest U_q(su(2))…
We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz is suitable for noncommutative…
The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are preserved. This model presents three…
The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$…
We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$.…
Higher spin Dirac operators on both the continuum sphere($S^2$) and its fuzzy analog($S^2_F$) come paired with anticommuting chirality operators. A consequence of this is seen in the fermion-like spectrum of these operators which is…
The Ginsparg-Wilson algebra is the algebra underlying the Ginsparg-Wilson solution of the fermion doubling problem in lattice gauge theory. The Dirac operator of the fuzzy sphere is not afflicted with this problem. Previously we have…
We find that there is an alternative possibility to define the chirality operator on the fuzzy sphere, due to the ambiguity of the operator ordering. Adopting this new chirality operator and the corresponding Dirac operator, we define…