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DOE OSTI · 1851256

4-manifolds and topological modular forms

Gukov, Sergei·Pei, Du·Putrov, Pavel·Vafa, Cumrun
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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.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSAnomalies in Field and String TheoriesConformal Field TheoryDifferential and Algebraic GeometryPhysicsTopological Field Theories

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Gukov, Sergei, Pei, Du, Putrov, Pavel, Vafa, Cumrun. 2021-05-11. 4-manifolds and topological modular forms. https://doi.org/10.1007/jhep05(2021)084

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