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تسجيل مستخدم جديدAxial anomaly in the reduced model: Higher representations
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تأليف
Teruaki Inagaki
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The topological charge in the $U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge field configurations which is termed $U(1)$ embedding.
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The axial anomaly arising from the fermion sector of $U(N)$ or $SU(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$U(1)$ embedding with $N=L^d$). We use the overlap-Dirac operator and consider how the an
omaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of $L^2$ (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general gauge-group representations in the large $N$ limit. The large $N$ limit exhibits expected algebraic properties as the axial anomaly. Nevertheless, when the gauge group is $SU(N)$, it does not have a structure such as the trace of a product of traceless gauge-group generators which is expected from the corresponding gauge field theory.
The spectral flow of the overlap operator is computed numerically along a path connecting two gauge fields which differ by a topologically non-trivial gauge transformation. The calculation is performed for SU(2) in the 3/2 and 5/2 representation. An
even-odd pattern for the spectral flow as predicted by Witten is verified. The results are, however, more complicated than naively expected.
The spectral flow of the overlap operator is computed numerically along a particular path in gauge field space. The path connects two gauge equivalent configurations which differ by a gauge transformation in the non-trivial class of pi_4(SU(2)). The
computation is done with the SU(2) gauge field in the fundamental, the 3/2, and the 5/2 representation. The number of eigenvalue pairs that change places along this path is established for these three representations and an even-odd pattern predicted by Witten is verified.
We present analytical results to guide numerical simulations with Wilson fermions in higher representations of the colour group. The ratio of $Lambda$ parameters, the additive renormalization of the fermion mass, and the renormalization of fermion bi
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In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition. Our simulation data also indicate suppression of topological susceptibili
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