Flux and charge quantization in 11-dimensional supergravity

Determine a fully consistent, non-perturbative flux- and charge-quantization law for the C-field in D=11, N=1 supergravity that fixes the global higher gauge field content (including torsion charges) and is compatible with the supergravity equations of motion.

Background

Flux and charge quantization is necessary to complete local higher gauge field descriptions to globally well-defined non-perturbative field theories, as it determines torsion charges and the global structure of gauge potentials.

For the 11d supergravity C-field, quantization had been discussed largely in the bosonic sector and without imposing the supergravity equations of motion. The paper proposes a duality-symmetric superspace formulation and shows how this naturally leads to a quantizable super C-field flux compatible with on-shell 11d supergravity.

References

In \S\ref{SuperFluxQuantization} we address the open problem of flux- and charge-quantization (see ) of $D=11$, $\mathcal{N}=1$ supergravity (11d SuGra , review in ), explaining how this is a necessary step towards the completion of 11d SuGra to the conjectured ``M-theory'' .

— Flux Quantization on 11-dimensional Superspace  (2403.16456 - Giotopoulos et al., 2024) in Overview and Results; Section 1 (Super-Flux Quantization of 11d SuGra)

Especially in the presence of Romans mass, RR flux quantisation is a subtle problem. At the level of supergravity, one usually imposes Page flux quantisation , which in our conventions ($2\pi\sqrt{\alpha'}=1$), and in the gauge $B_2=0$ used here, amounts to requiring $\int_C F_4\in\mathbb Z$ for every integral 4-cycle $C\subset X_8$, i.e. $[F_4]\in H4(X_8,\mathbb Z)$. For a purely untwisted flux, we derive candidate Page quantisation conditions from the fourteen explicit orbifold coordinate cycles constructed below. Interpreting these conditions as Page quantisation conditions on the smooth resolution requires the additional assumption that these orbifold cycles lift to integral 4-cycles of $X_8$ and that the periods of the untwisted forms are unchanged under this lift. Nevertheless, more refined RR quantisation conditions have been formulated . Since we are unable to implement them explicitly for our toroidal example, we restrict ourselves to Page flux quantisation.

— Type IIA on Spin(7) manifolds with fluxes  (2608.18284 - Cribiori et al., 18 Aug 2026) in Section 2, subsection A smooth resolution and the normalisation of bulk forms

This proves an equality of local eight-form classes, while the corresponding global anomaly analysis is left for future work.

— Perturbative Anomaly Inflow on Orbifolds  (2608.23326 - Zhang, 24 Aug 2026) in Section 1, subsection “Outline of the inflow derivation”; paragraph following equation (1.25), and Section 5, paragraph “Limitations regarding non-perturbative anomalies”