SL (2 , C) group action on cohomological field theories

Alexey Basalaev

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish
Pages (from-to)161-183
Number of pages23
JournalLetters in Mathematical Physics
Issue number1
Publication statusPublished - 1 Jan 2018
Externally publishedYes


  • Cohomological field theories
  • Givental’s action
  • Primitive forms
  • Total ancestor potential


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