arXiv research

We consider the hypothesis that the C-field 4-flux and 7-flux forms in M-theory are in the image of the non-abelian Chern character map from the non-abelian generalized cohomology theory called J-twisted Cohomotopy theory. We prove for M2-brane backgrounds in M-theory on 8-manifolds that such charge quantization of the…

11D supergravity completes with quantized C-field flux.

The higher gauge field in 11-dimensional supergravity -- the C-field -- is constrained by quantum effects to be a cocycle in some twisted version of differential cohomology. We argue that it should indeed be a cocycle in a certain twisted nonabelian differential cohomology. We give a simple and natural characterization…

Resolves anomaly cancellation for M5-brane in M-theory.

The paper explores how fields in higher dimensions are quantized.

We consider geometric and analytical aspects of M-theory on a manifold with boundary Y. The partition function of the C-field requires summing over harmonic forms. When Y is closed Hodge theory gives a unique harmonic form in each de Rham cohomology class, while in the presence of a boundary the Hodge-Morrey-Friedrichs…

We uncover and highlight relations between the M-branes in M-theory and various topological invariants: the Hopf invariant over $\mathbb{Q}$, $\mathbb{Z}$ and $\mathbb{Z}_2$, the Kervaire invariant, the $f$-invariant, and the $ν$-invariant. This requires either a framing or a corner structure. The canonical framing pro…

Cohomotopy charge quantization implies String structure on M5-branes.

The actions, anomalies, and quantization conditions allow the M2-brane and the M5-brane to support, in a natural way, structures beyond Spin on their worldvolumes. The main examples are twisted String structures. This also extends to twisted String^c structures, which we introduce and relate to twisted String structure…

The full 6d Hopf-Wess-Zumino term in the action functional for the M5-brane is anomalous as traditionally defined. What has been missing is a condition implying the higher analogue of level quantization familiar from the 2d Wess-Zumino term. We prove that the anomaly cancellation condition is implied by the hypothesis …

Modernizes higher-dimensional supergravity, linking it to flux quantization.

In anomaly-free quantum field theories the integrand in the bosonic functional integral--the exponential of the effective action after integrating out fermions--is often defined only up to a phase without an additional choice. We term this choice ``setting the quantum integrand''. In the low-energy approximation to M-t…

The equations of motion and the Bianchi identity of the C-field in M-theory are encoded in terms of the signature operator. We then reformulate the topological part of the action in M-theory using the signature, which leads to connections to the geometry of the underlying manifold, including positive scalar curvature. …

Analyzes quantization of flux observables in gauge theories.

Differential Cohomotopy theory predicts brane interactions via chord diagrams.

In the quest for the mathematical formulation of M-theory, we consider three major open problems: a first-principles construction of the single (abelian) M5-brane Lagrangian density, the origin of the gauge field in heterotic M-theory, and the supersymmetric enhancement of exceptional M-geometry. By combining technique…

10D IIA Superspace is put on shell by imposing duality-symmetric Bianchi identities on super-flux densities.

There are fundamental open problems in the precise global nature of RR-field tadpole cancellation conditions in string theory. Moreover, the non-perturbative lift as M5/MO5-anomaly cancellation in M-theory had been based on indirect plausibility arguments,lacking a microscopic underpinning in M-brane charge quantizatio…

We study the effects of having multiple Spin structures on the partition function of the spacetime fields in M-theory. This leads to a potential anomaly which appears in the eta-invariants upon variation of the Spin structure. The main source of such spaces are manifolds with nontrivial fundamental group, which are als…

New method for flux quantization on phase space stacks.