Continuum scaling limit and conformal field theory correspondence of dual-unitary circuits

Establish the continuum scaling limit of dual-unitary brickwork circuits in which both space and time become continuous, and rigorously determine the resulting conformally invariant field theory and its precise correspondence with the discrete dual-unitary dynamics.

Background

Dual-unitary circuits treat space and time on an equal footing, suggesting an emergent conformal invariance in a continuum limit. Various observations point toward connections with conformal field theory, holography, and emergent dual-unitarity near conformal fixed points.

A full, rigorous derivation of a conformal field theory emerging from dual-unitary dynamics in the scaling limit, along with a precise mapping, is not yet available.