Title: Holographic Complexity from Group Cohomology

Speaker: Bartek Czech (Tsinghua)

Time: 11:30-12:05 (GMT+0), 2021.08.04

Abstract:

I outline a principled way to define state complexity in holographic field theories. The physical starting point is subregion duality and the key mathematical concept is group cohomology. The group in question maps cutoff-sized entanglement wedges to one another. The physical content of the cocycle condition is that complexity should be independent of RG scheme (holographically: of radial slicing). I use the cluster state, which has Symmetry-Protected Topological (SPT) order and which serves as a resource for Measurement-Based Quantum Computing (MBQC), to illustrate the proposal in a toy model. Group cohomology does not provide a unique definition of complexity, but a linear space of admissible complexity measures.