Abstract
In symplectic field theory (SFT), the moduli spaces of J-holomorphic curves can be oriented coherently (i.e., in a manner compatible with gluing). In this note, we correct the signs involved in the generating function \(\textbf{H}\) in SFT so that the master equation \(\textbf{H}\cdot \textbf{H}= 0\) holds assuming transversality. The orientation convention that we use is consistent with that of Hutchings–Taubes from (J Symplectic Geom 7(1):29–133, 2009), but differs from that of Bourgeois–Mohnke in (Math Z 248(1):123–146, 2004).
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Notes
The matching ordering between the negative punctures of \(\dot{\Sigma }\) and the positive punctures of \(\dot{\Sigma }'\) is reversed in [4].
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Acknowledgements
We thank Ko Honda, Russell Avdek, and Fan Zheng for helpful discussions. We also thank anonymous referee for their helpful feedback, which has greatly improved the clarity of this paper.
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Bao, E. Coherent orientations in symplectic field theory revisited. Math. Z. 305, 30 (2023). https://doi.org/10.1007/s00209-023-03366-8
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DOI: https://doi.org/10.1007/s00209-023-03366-8