# Practical consequences of the geometric cobordism hypothesis

As far as I understand, the cobordism hypothesis provides a construction of all (appropriately defined) fully-extended TQFTs. In particular, given a fully-dualizable object in a certain category, one can in principle construct the entire TQFT (e.g. the partition function on an arbitrary closed manifold of full dimensionality).

I recently came across the work of Grady and Pavlov, where they claim a proof of the geometric cobordism hypothesis, which should be an analogous statement for arbitrary quantum field theories (i.e. not necessarily topological ones).

My question is: does this lead to a more-or-less explicit construction of any non-trivial quantum field theories? If so, this would be extremely interesting since only a handful of interacting quantum field theories have been constructed in more than two dimensions, and none in more than three dimensions.

A related question is: Are there any tools in the work of Grady and Pavlov (or elsewhere in the literature) that allow one to compute any interesting quantities in non-trivial quantum field theories in more than two dimensions? An example of such a quantity would be the spectrum of the Hamiltonian on a given codimension-1 manifold.

I would be happy to hear any relevant comments, and dispelling of confusions I might have about what has been achieved in this line of developments.

One explicit example can be found on page 112 of the slides http://dmitripavlov.org/lecture-1.pdf. Given a Lie group $$G$$, a level for $$G$$, and an invariant polynomial of degree 2 on the Lie algebra of $$G$$, it constructs the prequantum Chern–Simons field theory as a fully extended 3-dimensional $$G$$-gauged functorial field theory. A paper with complete proofs is forthcoming.