Cut-and-join operators in cohomological field theory and topological recursion

• Alexander Alexandrov ^[1]
  1. [1] Center for Geometry and Physics, Institute for Basic Science (IBS), Korea
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-44
• Idioma: inglés
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• Resumen

  • We construct a cubic cut-and-join operator description for the partition function of the Chekhov–Eynard–Orantin topological recursion for a local spectral curve with simple ramification points. In particular, this class contains partition functions of all semisimple cohomological field theories. The cut-and-join description leads to an algebraic version of topological recursion. For the same partition functions we also derive N families of the Virasoro constraints and prove that these constraints, supplemented by a deformed dimension constraint, imply the cut-and-join description.