Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-03-24
JHEP0609:037,2006
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 6 figures, more references added
Scientific paper
10.1088/1126-6708/2006/09/037
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 Dirac operator on the q-deformed fuzzy sphere-$S_{qF}^{2}(N)$ using the spinor modules of $\uq$. We explicitly obtain the zero modes and also calculate the spectrum for this Dirac operator. Using this Dirac operator, we construct the $\uq$ invariant action for the spinor fields on $S_{qF}^{2}(N)$ which are regularised and have only finite modes. We analyse the spectrum for both $q$ being root of unity and real, showing interesting features like its novel degeneracy. We also study various limits of the parameter space (q, N) and recover the known spectrum in both fuzzy and commutative sphere.
Harikumar E.
Queiroz Amilcar R.
Teotonio-Sobrinho Paulo
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