Are there tensor models in higher dimensions?

Tensor models refer to theories based on fields with more than two
indices. Examples include theories with O(N)^3 symmetry. Such theories
can lead to new large N limits whose physics differs from the more
familiar vector model and adjoint (or matrix) large N limits, as we
will review in the talk. While large N tensor models seem to exist in
0d and 1d, , which have a great deal of formal similarity with the SYK
model, the question of whether it is possible to construct interacting
conformal tensor models in higher dimensions is still open. We will
describe how many natural attempts to construct higher dimensional
versions of these theories with conformal invariance leads to
difficulties.