Description
Several works have pointed out the similarities between
properties of hierarchical tensor network descriptions of
critical systems and their gravitational duals. Though the
body of circumstantial evidence for this link is compelling,
it is difficult to make these notions concrete due to the
different language of the two areas. Here, I outline a first
step towards bridging this language barrier, by explicitly
constructing a field theory over the simplest tensor network
states - matrix product states. I develop a functional
integral representation of the partition function of a spin
chain, where the measure of integration is explicitly over
matrix product tensors. I will discuss the potential
applications of such a field theory and the challenge
presented by extending these ideas to critical systems, to
higher dimensions and to hierarchical tensor networks.
(Andrew G Green, C. A. Hooley, J. Keeling and S. H. Simon)
