4-manifolds and topological modular forms

Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun

doi:10.1007/JHEP05(2021)084

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4-manifolds and topological modular forms

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Gukov, Sergei
Max Planck Institute for Mathematics, Max Planck Society;

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Citation

Gukov, S., Pei, D., Putrov, P., & Vafa, C. (2021). 4-manifolds and topological modular forms. Journal of High Energy Physics, 2021(5): 84. doi:10.1007/JHEP05(2021)084.

Cite as: https://hdl.handle.net/21.11116/0000-0008-B52A-D

Abstract

We build a connection between topology of smooth 4-manifolds and the theory
of topological modular forms by considering topologically twisted
compactification of 6d (1,0) theories on 4-manifolds with flavor symmetry
backgrounds. The effective 2d theory has (0,1) supersymmetry and, possibly, a
residual flavor symmetry. The equivariant topological Witten genus of this 2d
theory then produces a new invariant of the 4-manifold equipped with a
principle bundle, valued in the ring of equivariant weakly holomorphic
(topological) modular forms. We describe basic properties of this map and
present a few simple examples. As a byproduct, we obtain some new results on 't
Hooft anomalies of 6d (1,0) theories and a better understanding of the relation
between 2d (0,1) theories and TMF spectra.