The sigma-model example conjecture for symmetric open-closed topological conformal field theories

A symmetric open-closed topological conformal field theory (OC TCFT) is a theory encoded by the relevant dg Batalin–Vilkovisky algebra and its operations on open and closed string states. The OC sigma model, including A-model or Gromov–Witten theory, is expected to produce a Gromov–Witten potential satisfying the quantum master equation.

Sigma-model example conjecture. Sigma model produces an example of a symmetric OC TCFT.

This expectation would connect open-closed sigma models and Gromov–Witten theory with the universal algebraic structure governing symmetric OC TCFTs. The supplied text presents it as a widely expected statement, without indicating that it has been proved or disproved.