Cohomological field theories with non-tautological classes

@article{Pandharipande2018CohomologicalFT,
  title={Cohomological field theories with non-tautological classes},
  author={R. Pandharipande and D. Zvonkine},
  journal={arXiv: Algebraic Geometry},
  year={2018}
}
A method of constructing Cohomological Field Theories (CohFTs) with unit using minimal classes on the moduli spaces of curves is developed. As a simple consequence, CohFTs with unit are found which take values outside of the tautological cohomology of the moduli spaces of curves. A study of minimal classes in low genus is presented in the Appendix by D. Petersen. 
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