tensor networks for quantum fields: conformal invariance and emergent de Sitter space

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the multi-scale entanglement renormalization ansatz (MERA) is a tensor network that efficiently represents the ground state wave-function of a lattice Hamiltonian. Similarly, its extension to the continuum, the continuous MERA [proposed by Haegeman, Osborne, Verschelde and Verstraete, Phys. Rev. Lett. 110, 100402 (2013), arXiv:1102.5524], aims to efficiently represent the vacuum state wave-functional of a quantum field theory. In this talk I will first review MERA and cMERA, with emphasis on why we should care about these two constructions, including their conjectured connection to the AdS/CFT correspondence. Then, using the simplified context of the free boson CFT in 1+1 dimensions, I will discuss two new results: (1) the cMERA wave-function, which has an explicit UV cut-off, is nevertheless invariant under the conformal group (but with modified Virasoro generators: the stress tensor is non-local at short distances); (2) cMERA can be regarded as an evolution in de Sitter space. Talk based on joint work with Qi Hu, in preparation.

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