Axial-vector coupling and chiral anomaly in the spectral quark model

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We studied the Adler-Bardeen-Bell-Jackiw anomaly in the context of a finite chiral quark model known as the spectral quark model. Within this model, we obtain the general nonlocal form of the axial vertex compatible with a nonvanishing axial coupling, in the chiral limit. The triangle anomaly is computed and we show that the obtained dependence of the axial vertex with the spectral mass is necessary to ensure both finiteness and the correct violation of the chiral Ward-Takahashi identity.