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We take a peek at a general program that associates vertex (or, chiral) algebras to smooth 4-manifolds in such a way that operations on algebras mirror gluing operations on 4-manifolds and, furthermore, equivalent constructions of 4-manifolds give rise to equivalences (dualities) of the corresponding algebras.
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D. Gaiotto, N=2 dualities , JHEP 1208
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P. Putrov, J. Song and W. Yan, (0,4) dualities , JHEP 1603
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S. Gukov, P. Putrov and C. Vafa, Fivebranes and 3-manifold homology , JHEP 1707
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B. L. Feigin, Extensions of vertex algebras. Constructions and applications , Usp. Mat. Nauk 72
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S. Gukov, Trisecting non-Lagrangian theories , JHEP 1711
2017
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M. Dedushenko, Chiral algebras in Landau-Ginzburg models, JHEP 1803
2018
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2018
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2018
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2018
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Y. Tanaka, A perturbation and generic smoothness of the Vafa-Witten moduli spaces on closed symplectic four-manifolds , Glasg. Math. J. 61
2019
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