Theoretical Physics Wednesday Seminar: Pavel Putrov

6d (1,0) theories on 4-manifolds

In my talk I will discuss topologically twisted compactification of 6d (1,0) theories on 4-manifolds with background flavor symmetry bundles. The effective 2d theory generically has (0,1) supersymmetry and a residual flavor symmetry. Evaluation of its elliptic genus thus produces an invariant of the 4-manifold equipped with a principle bundle valued in the ring of (equivariant) modular forms. By further including torsion valued invariants of (0,1) 2d theories, one obtains an invariant of 4-manifolds valued in (equivariant) topological modular forms (TMF). I will describe basic properties of this map and present a few simple examples. I will also mention some new results on 't Hooft anomalies of 6d (1,0) theories. The talk is based on a joint work with Gukov, Pei and Vafa.