Dirac operator on the q-deformed fuzzy sphere and its spectrum

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 actionof $\uq$ and in the limit $q\to 1$, it reduces to the fuzzy sphere$S_{F}^2(N)$. We construct the Dirac operator on the q-deformed fuzzysphere-$S_{qF}^{2}(N)$ using the spinor modules of $\uq$. We explicitly obtainthe zero modes and also calculate the spectrum for this Dirac operator. Usingthis Dirac operator, we construct the $\uq$ invariant action for the spinorfields on $S_{qF}^{2}(N)$ which are regularised and have only finite modes. Weanalyse the spectrum for both $q$ being root of unity and real, showinginteresting features like its novel degeneracy. We also study various limits ofthe parameter space (q, N) and recover the known spectrum in both fuzzy andcommutative sphere.Comment: 19 pages, 6 figures, more references adde