String, dilaton and divisor equation in Symplectic Field Theory

TL;DR

This paper explores the algebraic structures in Symplectic Field Theory, introducing gravitational descendants and deriving new differential equations for the Hamiltonian, highlighting their dependence on auxiliary data choices.

Contribution

It generalizes gravitational descendants in SFT and establishes their role in generating symmetries and differential equations, extending concepts from Gromov-Witten theory.

Findings

Defined a generalization of gravitational descendants in SFT

Derived new differential equations for the SFT Hamiltonian

Analyzed dependence on auxiliary data choices

Abstract

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.