Nijenhuis operator in contact homology and descendant recursion in symplectic field theory

Details Nijenhuis operator in contact homology and descendant recursion in symplectic field theory Nijenhuis operator in contact homology and descendant recursion in symplectic field theory

2012-01-05

arxiv.org/abs/1201.1127v2

Mathematics

Symplectic Geometry

24 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:0907.0789 by other author

Scientific paper

In this paper we investigate the algebraic structure related to a new type of correlator associated to the moduli spaces of $S^1$-parametrized curves in contact homology and rational symplectic field theory. Such correlators are the natural generalization of the non-equivariant linearized contact homology differential (after Bourgeois-Oancea) and give rise to an invariant Nijenhuis (or hereditary) operator (\`a la Magri-Fuchsteiner) in contact homology which recovers the descendant theory from the primaries. We also show how such structure generalizes to the full SFT Poisson homology algebra to a (graded symmetric) bivector. The descendant hamiltonians satisfy to recursion relations, analogous to bihamiltonian recursion, with respect to the pair formed by the natural Poisson structure in SFT and such bivector.

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