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Categorification of 2d–4d wall-crossing and curve-valued Landau–Ginzburg potentials

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Abstract

In this paper, we propose definitions of categorical enhancements of the data involved in the 2d–4d wall-crossing formulas which generalize both Cecotti–Vafa and Kontsevich–Soibelman motivic wall-crossing formulas. We consider several examples of this enhancement, including a Fukaya–Seidel category over a general curve.

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Notes

  1. Some hints in this direction can be found in arXiv:1506.04086

  2. In fact, the framework of [11, Sect. 2] covers all types of wall-crossing formulas, including 2d, 4d, and 2d–4d. However, the tradition in the physics literature is to call 2d wall-crossing formulas “Cecotti–Vafa WCF,” while 4d wall-crossing formulas are called “Kontsevich–Soibelman WCF.”

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Acknowledgements

We thank E. Diaconescu and M. Kontsevich for useful discussions on the topic. In particular, our geometric example is a result of the rethinking of the physically motivated computations made by Diaconescu. We also wish to thank the referee for their valuable comments and corrections. Y.S. thanks IHES for excellent research conditions. His work was partially supported by an NSF grant and by Simu-Munson Star Excellence award of KSU. G.K. was partially supported by a Simons collaboration grant.

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  1. Kansas State University, Manhattan, USA

    Gabriel Kerr & Yan Soibelman

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  1. Gabriel Kerr
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  2. Yan Soibelman
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Correspondence to Gabriel Kerr.

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Kerr, G., Soibelman, Y. Categorification of 2d–4d wall-crossing and curve-valued Landau–Ginzburg potentials. Lett Math Phys 112, 47 (2022). https://doi.org/10.1007/s11005-022-01535-0

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