Topological sectors for heterotic M5-brane charges under Hypothesis H

A bstract Assuming Fiorenza-Sati-Schreiber’s Hypothesis H, on the charge quantization of M-theory’s C -field, the topological sectors of the resulting String c 2 (4)-valued higher gauge theory on a heterotic M5-brane are classified by homotopy classes of maps from the worldvolume Σ M 5 to B String c 2 (4). This note calculates the sectors in a number of examples of M5-brane topology, including examples considered in the 3d-3d correspondence, the emergence of skyrmions from higher-dimensional instantons and Witten’s analysis of the S-duality of 4d Yang-Mills theory.