Abstract
We explain how dispersionless integrable hierarchy in 2d topological field theory arises from the Kodaira–Spencer gravity (BCOV theory). The infinitely many commuting Hamiltonians are given by the current observables associated to the infinite abelian symmetries of the Kodaira–Spencer gravity. We describe a BV framework of effective field theories that leads to the B-model interpretation of dispersionless integrable hierarchy.
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Acknowledgements
The work of W.H. is partially supported by grant 11901597 of NSFC. The work of S.L. is partially supported by grant 11801300 of NSFC and grant Z180003 of Beijing Natural Science Foundation. The work of X.T. is partially supported by Tsinghua Postdoc Grant 100410058. Part of this work was done while S.L. was visiting Institute for Advanced Study in Fall 2019. S.L. thanks for their hospitality and provision of excellent working environment.
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He, W., Li, S., Tang, X. et al. Dispersionless Integrable Hierarchy via Kodaira–Spencer Gravity. Commun. Math. Phys. 379, 327–352 (2020). https://doi.org/10.1007/s00220-020-03809-x
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DOI: https://doi.org/10.1007/s00220-020-03809-x