Topological sectors for heterotic M5-brane charges under Hypothesis H

David Michael Roberts

doi:10.1007/jhep06(2020)052

Abstract

Assuming Fiorenza-Sati-Schreiber’s Hypothesis H, on the charge quantization of M-theory’s C -field, the topological sectors of the resulting Stringc2 (4)-valued higher gauge theory on a heterotic M5-brane are classified by homotopy classes of maps from the worldvolume ΣM5 to BStringc2 (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.

Highlights

The sectors are in bijection with homotopy classes of such maps, where two maps c0, c1 are homotopic if there is a continuous family of maps ct : X → BG, 0 ≤ t ≤ 1
Assuming Fiorenza-Sati-Schreiber’s Hypothesis H, on the charge quantization of M-theory’s C-field, the topological sectors of the resulting Stringc2(4)-valued higher gauge theory on a heterotic M5-brane are classified by homotopy classes of maps from the worldvolume ΣM5 to BStringc2(4)
This purely mathematical hypothesis has been shown [14, 16,17,18,19,20,21] to imply a host of anomaly cancellation and other consistency conditions previously proposed in the literature on physical grounds

Summary

Introduction

The sectors are in bijection with homotopy classes of such maps, where two maps c0, c1 are homotopic if there is a continuous family of maps ct : X → BG, 0 ≤ t ≤ 1. For the topological sector analysis we present here, knowing the classifying space is sufficient, as we need to calculate the homotopy classes of maps to B Stringc2(4). The reason that this family of 2-groups, or the 2-group Stringc2(4), is of interest, is that from Hypothesis H [13, 14] it follows that a heterotic M5-brane [15] automatically carries fields from the higher gauge theory with Stringc2(4) as the structure 2-group [16]. This purely mathematical hypothesis has been shown [14, 16,17,18,19,20,21] to imply a host of anomaly cancellation and other consistency conditions previously proposed in the literature on physical grounds

Results

Discussion

Conclusion