SL(2,C) action on cohomological field theories
The role of modular forms in Gromov-Witten theory was first observed by physicists and later approved by mathematicians. It was shown in particular by Milanov-Ruan-Shen that the coefficients of the genus g GW potential of the certain orbifolds could be treated as the quasi-modular forms. This motivates existence of the SL(2,C)-action on the entire partition function. Using Givental's action we introduce SL(2,C)-action on the partition functions of the CohFTs. By applying the graphical calculus of D. Zvonkine we compute explicitly the Givental's action found on the partition function of a CohFT.