Many aspects of the theory of “topological strings” (the A-model and the B-model) proceed in close analogy (just simpler) to the “physical” string theory. Accordingly, as the latter can usefully be organized as the dimensional reduction of a conjectured UV-completion of 11-dimensional supergravity – M-theory – there seems to be an analogous higher dimensional organizational principle for topological strings, hence termed topological M-theory.
One way to understand it is as a TQFT-analog of the M2-brane sigma-model, the topological membrane.
The notion has been introduced in
Andrew Neitzke, Cumrun Vafa, section 7 of_Topological strings and their physical applications_, hep-th/0410178
Robbert Dijkgraaf, Sergei Gukov, Andrew Neitzke, Cumrun Vafa, Topological M-theory as Unification of Form Theories of Gravity (arXiv:hep-th/0411073)
Under the term “Z-theory” aspects were discussed in
An introduction is in
The topological membrane is made explicit in