The factorization-algebra Noether theorem

Let $\cT$ be a quantum field theory on a manifold $M$, and let $X$ be a sheaf of derived stacks on $M$. A factorizing line bundle on the prefactorization space $X_c$ is a line bundle with coherent isomorphisms compatible with the factorization products. The notation $\Dist_{X_c}^{\mc{L}}$ denotes distributions on $X_c$ twisted by such a line bundle, and $\Obs_\cT$ denotes the prefactorization algebra of observables of $\cT$.

Non-perturbative Noether theorem. If $\cT$ has $X$-symmetry, then there exists a factorizing line bundle $\mc{L}$ on the prefactorization space $X_c$ and a map of prefactorization algebras

$$J: \Dist_{X_c}^{\mc{L}} \to \Obs_\cT.$$

This is proposed as the non-perturbative analogue of Noether's theorem for quantum field theories. The factorizing line bundle incorporates possible ’t Hooft anomalies, while the map sends the corresponding twisted distributions to observables. The source excerpt does not establish the assertion or state a resolution, so its status is open.