Aarhus Universitets segl

4-manifolds and topological modular forms

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  • Sergei Gukov, California Institute of Technology, Max Planck Institute for Mathematics
  • ,
  • Du Pei, California Institute of Technology
  • ,
  • Pavel Putrov, International Centre for Theoretical Physics (ICTP), Trieste, Princeton University
  • ,
  • Cumrun Vafa, Harvard University

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.

TidsskriftJournal of High Energy Physics
StatusUdgivet - maj 2021

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