4-manifolds and topological modular forms

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