Coherent orientations in symplectic field theory revisited

TL;DR

This paper revisits the orientation conventions in symplectic field theory, correcting sign issues in the generating function to ensure the master equation holds, aligning with Hutchings-Taubes' approach.

Contribution

It provides a corrected orientation framework in SFT that guarantees the validity of the master equation under transversality assumptions.

Findings

Corrected signs in the generating function $ extbf{H}$

Ensured the master equation $ extbf{H} imes extbf{H} = 0$ holds

Aligned orientation conventions with Hutchings-Taubes

Abstract

In symplectic field theory (SFT), the moduli spaces of $J$-holomorphic curves can be oriented coherently (compatible with gluing). In this note, we correct the signs involved in the generating function $\mathbf H$ in SFT so that the master equation $\mathbf H \cdot \mathbf H = 0$ holds assuming transversality. The orientation convention that we use is consistent with that of Hutchings-Taubes from [HT09].