We introduce the SL(2, C) group action on a partition function of a coho-mological 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 P 1 and quasi-modular forms, arXiv:1106.2321, 2011).

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