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## SL(2,C) group action on Cohomological field theories

Letters in Mathematical Physics. 2018. Vol. 108. No. 1. P. 161-183.

We introduce the SL(2, C) group action on the partition function of the Cohomological field theory via the certain Givental's action. Restricted to the small phase space we describe the action via the explicit formulae on the CohFT genus g potential. We prove that applied to the total ancestor potential of the simple elliptic singularity the action introduced coincides with the transformation of Milanov-Ruan changing the primitive form (c.f. http://arxiv.org/abs/1106.2321).