High Energy Theory Seminar
The multiscale entanglement renormalization ansatz (MERA) is a 2 dimensional tensor network that describes the ground state of a critical quantum spin chain (or vacuum of a 2d CFT on the lattice). In 2009, Swingle argued that MERA is a lattice realization of the AdS/CFT correspondence, with the tensor network representing a time slice of AdS, namely hyperbolic space H2. Other authors have since then argued that, instead, MERA represents de Sitter spacetime dS2. I will introduce a criterion, based on CFT path integrals, to unambiguously assign a geometry to a tensor network and then conclude that MERA is neither H2 nor dS2, but actually a light cone L2. Finally, I will introduce two new tensor networks, euclidean MERA and lorentzian MERA, corresponding to H2 and dS2 and discuss the implications of these results for holography and the study of quantum field theory in curved spacetime.