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Using self dual Ashtekar variables, we investigate (at the effective level)the spherically symmetry reduced model of loop quantum gravity, both in vacuumand when coupled to a scalar field. Within the real Ashtekar-Barberoformulation, the system scalar field coupled to spherically symmetric gravityis known to possess a non closed (quantum) algebra of constraints once theholonomy corrections are introduced, which forbids the loop quantization of themodel. Moreover, the vacuum case, while not anomalous, introduces modificationswhich are usually interpreted as an effective signature change of the metric inthe deep quantum region. We show in this paper that both those complicationsdisappear when working with self dual Ashtekar variables, both in the vacuumcase and in the case of gravity minimally coupled to a scalar field. In thisframework, the algebra of the holonomy corrected constraints is anomaly freeand reproduces the classical hypersurface deformation algebra without anydeformations. A possible path towards quantization of this model is brieflydiscussed.

Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections