Flux Quantization on 11-dimensional Superspace
Grigorios Giotopoulos, Hisham Sati, Urs Schreiber
TL;DR
This work shows that flux quantization of the 11d C-field is naturally achieved by a duality-symmetric formulation on superspace, where the bosonic flux densities $(G_4,G_7)$ obey $dG_4=0$ and $dG_7= frac{1}{2}G_4\u2227 G_4$, while superspace extensions $(G_4^s,G_7^s)$ absorb the Hodge duality constraint into pre-metric Bianchi identities. By developing a framework of higher, smooth super geometry and super Cartan geometry, the authors identify the universal flux-quantization data with a Whitehead $L_infty$-algebra isomorphic to the rational model of the 4-sphere, enabling flux quantization to lift to superfields via a classifying space $ rak{A}$ with $ rak{l} rak{A} rak{a}$. They prove that on an $(11|f{32})$-dimensional super-spacetime, quantized super-C-field flux automatically enforces the on-shell equations of motion of 11d supergravity (Maxwell for $G_4$, Rarita–Schwinger for the gravitino, and Einstein gravity), with rheonomy ensuring a consistent extension from the bosonic body to the full superfield content. The results unify flux quantization with the UV completion program for M-theory, and suggest a path toward exotic geometries and brane physics (e.g., M5) within a higher super-geometric, flux-quantized context.
Abstract
Flux quantization of the C-field in 11d supergravity is arguably necessary for the (UV-)completion of the theory, in that it determines the torsion charges carried by small numbers of M-branes. However, hypotheses about C-field flux-quantization ("models of the C-field") have previously been discussed only in the bosonic sector of 11d supergravity and ignoring the supergravity equations of motion. Here we highlight a duality-symmetric formulation of on-shell 11d supergravity on superspace, observe that this naturally lends itself to completion of the theory by flux quantization, and indeed that 11d super-spacetimes are put on-shell by carrying quantizable duality-symmetric super-C-field flux; the proof of which we present in detail.