SL (2, C) group action on cohomological field theories - Basalaev, Alexey (Letters in mathematical physics, 2018)
We introduce the SL(2,C) group action on a partition function of a cohomological field theory via a certain Givental’s action. Restricted to the small phase space we describe the action via the explicit formulae on a CohFT genus g potential. We prove that applied to the total ancestor potential of a simple-elliptic singularity the action introduced coincides with the transformation of Milanov–Ruan changing the primitive form (cf. Milanov and Ruan in Gromov–Witten theory of elliptic orbifold P1 and quasi-modular forms, arXiv:1106.2321, 2011).