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The continuum limit of tensor networks: a path integral representation

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I will discuss a
path-integral representation of continuum tensor networks that extends the
continuous MPS class for 1-D quantum fields to arbitrary spatial dimensions
while encoding desirable symmetries. The physical states can be interpreted as
arising through a continuous measurement process by a lower dimensional virtual
field with Lorentz symmetry. The resultant physical states naturally obey
entropy area laws, with the expectation values of observables determined by the
dissipative dynamics of the boundary field. The class offers the prospect of
powerful new analytical and computational tools to describe the physics of
strongly interacting field systems.