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Article
Open AccessFlux quantization on 11-dimensional superspace
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 N ≪ ∞ of M-branes. However, hyp...
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Article
Topological Quantum Gates in Homotopy Type Theory
Despite the plausible necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of topological quantum logic gates had arguably remained shaky, both regarding t...
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Article
Flux Quantization on Phase Space
While it has become widely appreciated that (higher) gauge theories need, besides their variational phase space data, to be equipped with “flux quantization laws” in generalized differential cohomology, there ...
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Article
Cyclification of Orbifolds
Inertia orbifolds homotopy-quotiented by rotation of geometric loops play a fundamental role not only in ordinary cyclic cohomology, but more recently in constructions of equivariant Tate-elliptic cohomology and ...
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Article
Fundamental weight systems are quantum states
Weight systems on chord diagrams play a central role in knot theory and Chern–Simons theory; and more recently in stringy quantum gravity. We highlight that the noncommutative algebra of horizontal chord diagr...
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Article
Mysterious Triality and Rational Homotopy Theory
Mysterious Duality has been discovered by Iqbal, Neitzke, and Vafa (Adv Theor Math Phys 5:769–808, 2002) as a convincing, yet mysterious correspondence between certain symmetry patterns in toroidal compactific...
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Article
Twisted cohomotopy implies M5-brane anomaly cancellation
We highlight what seems to be a remaining subtlety in the argument for the cancellation of the total anomaly associated with the M5-brane in M-theory. Then, we prove that this subtlety is resolved under the hy...
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Article
Twisted Cohomotopy Implies Level Quantization of the Full 6d Wess-Zumino Term of the M5-Brane
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 famili...
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Article
Twisted Cohomotopy Implies M-Theory Anomaly Cancellation on 8-Manifolds
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 Cohom...
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Article
Open AccessSuper-exceptional geometry: origin of heterotic M-theory and super-exceptional embedding construction of M5
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 fi...
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Article
Real ADE-Equivariant (co)Homotopy and Super M-Branes
A key open problem in M-theory is the identification of the degrees of freedom that are expected to be hidden at ADE-singularities in spacetime. Comparison with the classification of D-branes by K-theory sugge...
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Article
Gauge Enhancement of Super M-Branes Via Parametrized Stable Homotopy Theory
A key open problem in M-theory is to explain the mechanism of “gauge enhancement” through which M-branes exhibit the nonabelian gauge degrees of freedom seen perturbatively in the limit of 10d string theory. I...
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Article
Twisted smooth Deligne cohomology
Deligne cohomology can be viewed as a differential refinement of integral cohomology, hence captures both topological and geometric information. On the other hand, it can be viewed as the simplest nontrivial v...
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Article
Massey products in differential cohomology via stacks
We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related ...
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Article
Open AccessLie n-algebras of BPS charges
We uncover higher algebraic structures on Noether currents and BPS charges. It is known that equivalence classes of conserved currents form a Lie algebra. We show that at least for target space symmetries of h...
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A Higher Stacky Perspective on Chern–Simons Theory
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern–Simons-type gauge field theories. We explain in some detail how the action ...
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Article
The E 8 Moduli 3-Stack of the C-Field in M-Theory
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 cocyc...
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Article
Twisted Differential String and Fivebrane Structures
In the background effective field theory of heterotic string theory, the Green-Schwarz anomaly cancellation mechanism plays a key role. Here we reinterpret it and its magnetic dual version in terms of, differenti...
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L ∞-Algebra Connections and Applications to String- and Chern-Simons n-Transport
We give a generalization of the notion of a Cartan-Ehresmann connection from Lie algebras to L ∞-algebras and use it to study the obstruction theory of lifts through higher String-like extension...
