# Higher symplectic capacities

## TL;DR

This paper introduces new symplectic capacities derived from rational symplectic field theory and contact homology, providing advanced tools for symplectic embedding obstructions with promising initial results.

## Contribution

It constructs novel symplectic capacities indexed by symmetric polynomials using rational symplectic field theory, expanding the toolkit for symplectic embedding problems.

## Key findings

- Capacities provide new obstructions to symplectic embeddings.
- Preliminary computations demonstrate their effectiveness in basic examples.
- Capacities exhibit important structural properties.

## Abstract

We construct new families of symplectic capacities indexed by certain symmetric polynomials, defined using rational symplectic field theory. In particular, we introduce a sequence of capacities based on an L-infinity structure on linearized contact homology and rational curve counts with local tangency constraints. We prove various structural properties of these capacities and give some preliminary computations which show that they give state of the art symplectic embedding obstructions in basic examples.