String, dilaton and divisor equation in Symplectic Field Theory

Details String, dilaton and divisor equation in Symplectic Field Theory String, dilaton and divisor equation in Symplectic Field Theory

2010-01-18

arxiv.org/abs/1001.3094v3

Mathematics

Symplectic Geometry

15 pages; corrected some imprecise and incomplete passages in the construction of the special coherent collection of sections,

Scientific paper

Infinite dimensional Hamiltonian systems appear naturally in the rich algebraic structure of Symplectic Field Theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an infinite number of symmetries of such systems . As in Gromov-Witten theory, the study of the topological meaning of gravitational descendants yields new differential equations for the SFT Hamiltonian, where the key point is to understand the dependence of the algebraic constructions on choices of auxiliary data like contact form, cylindrical almost complex structure, abstract perturbations, differential forms and coherent collections of sections used to define gravitational descendants.

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