T-duality and bosonization as examples of continuum gauging and disentangling

Dualities and duality transformations form a well established methodology in various aspects of quantum many body physics and quantum field theories, allowing one to exploit equivalence between models which may naively seem completely different in order to gain access to further physical regimes, either analytically, numerically or experimentally. Recently, in the context of condensed matter physics and quantum information, it was shown that dualities can be understood very well through a gauging and disentangling procedure that can be represented by a finite depth quantum circuit. In this letter we expand these concepts to the continuum, suggesting them as a way to derive duality transformations in continuum field theories and particle physics, and benchmark the presented ideas through the re-derivation of T-duality and bosonization.