In gauge theories, there is an inherent tension between locality and gauge invariance. This is precisely expressed by the failure to factorize the physical Hilbert space into local tensor products. The extended Hilbert space offers a resolution to this problem by embedding physical states into a larger Hilbert space containing gauge variant degrees of freedom. For two-dimensional Topological Quantum Field Theories (TQFTs), the speaker’s research team show how this extension fits inside the framework of extended quantum field theory (QFT), as described by the Moore-Segal axioms. Originally formulated for D-branes, they apply these axioms to the entanglement edge modes of the extended Hilbert space. For the case of two-dimensional Yang-Mills and its string theory dual, they demonstrate how this framework leads to exact calculations of multi-interval modular flow, negativity, and entanglement entropy. Moreover, an axiomatic formulation of the "entanglement brane" will be given, which nicely compliments the worldsheet description given in previous works.
