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Torsion Pontryagin Duality for the M-Theory C-Field
Topological sectors of the M-theory 3-form gauge potential (C_3) and its 4-form field strength (G_4) are known to carry subtle quantum phases and anomaly constraints, already visible in the shifted flux quantization and in the global definition of the effective action. (arXiv) A particularly rich and comparatively under-systematized component arises from torsion in the integral (co)homology of the compactification manifold: torsion classes define discrete fluxes, discrete gauge symmetries, and higher-form symmetry data in the effective theory. This article proposes a concrete conjectural organizing principle for these torsion sectors, termed Torsion Pontryagin Duality (TPD). The conjecture states that the torsion sectors admit a canonical finite Heisenberg-group structure, and that the “(C)-holonomy basis” and “(G)-flux basis” are related by a discrete Fourier transform whose kernel is the torsion linking pairing. This perspective unifies several phenomena: noncommutativity of torsion electric and magnetic flux measurements, universal (BF)-type symmetry topological field theories in the effective description, and a brane-braiding interpretation in terms of wrapped M2 and M5 branes. (arXiv)
