When do two different looking quantum field theories describe the same physics? This is essentially asking when the quantum field theories are isomorphic. In the case of topological quantum field theories, there are sometimes a way to determine them via topological invariants. For a superconformal field theory, what would be the minimal set of “invariants” to determine when they are isomorphic? I will discuss some approaches to this question in the context of superconformal field theories in four and six dimensions. Utilizing 4d class S theories that also admits 6d (1,0) SCFT origins, I will explain how a certain class of 4d N=2 SCFTs, which a priori look like distinct theories, can be shown to describe the same physics. I will further explain how the 6d (1,0) origin sheds light on the 3d duality.

Quantum error correction provides a convenient setup where bulk operators are defined only on a code subspace of the physical Hilbert space of the conformal field theory. I will first reformulate entanglement wedge reconstruction in the language of operator-algebra quantum error correction with infinite-dimensional physical and code Hilbert spaces. I will streamline my proof that for infinite-dimensional Hilbert spaces, the entanglement wedge reconstruction is identical to the equivalence of the boundary and bulk relative entropies. I will discuss its implications for holographic theories with the Reeh-Schlieder theorem.