M5-brane source charges, Chern--Connes pairings and noncommutative compactifications
Abstract
We formulate a source-adapted Chern--Connes description of M5-brane magnetic charge in physically motivated noncommutative and quotient linking sectors. The starting point is the local codimension-five geometry of an M5-brane source: the magnetic charge is measured on a four-dimensional link. In the smooth local model the link is the ordinary four-sphere, and the pairing reduces to the standard flux integral of the M-theory four-form field strength. The construction is motivated by the published even-codimensional Noncommutative Foliation Invariant (NCFI for short), where Connes' transverse fundamental cyclic cocycle is paired with an even transverse-geometric K-class. For an M5-brane the relevant codimension is odd, so the required odd K-class is supplied instead by the boundary map of the source/linking extension. Noncommutative or groupoid algebras are used only when they arise from physical mechanisms: Matrix/M-theory compactification on noncommutative tori, reduction to D-branes in background B-fields, large C-field M5 limits, or quotient/orbifold source links. The result is a topological charge formula, not a derivation of the full M5-brane dynamics or of the complete M-theory action.
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BibTeX
@misc{zois2026m5brane,
title = {{M5-brane source charges, Chern--Connes pairings and noncommutative compactifications}},
author = {Ioannis P. Zois},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31674},
eprint = {2610.31674},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31674},
}
RIS
TY - UNPB
TI - M5-brane source charges, Chern--Connes pairings and noncommutative compactifications
AU - Ioannis P. Zois
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.31674
UR - https://arxiv.org/abs/2610.31674
AB - We formulate a source-adapted Chern--Connes description of M5-brane magnetic charge in physically motivated noncommutative and quotient linking sectors. The starting point is the local codimension-five geometry of an M5-brane source: the magnetic charge is measured on a four-dimensional link. In the smooth local model the link is the ordinary four-sphere, and the pairing reduces to the standard flux integral of the M-theory four-form field strength. The construction is motivated by the published even-codimensional Noncommutative Foliation Invariant (NCFI for short), where Connes' transverse fundamental cyclic cocycle is paired with an even transverse-geometric K-class. For an M5-brane the relevant codimension is odd, so the required odd K-class is supplied instead by the boundary map of the source/linking extension. Noncommutative or groupoid algebras are used only when they arise from physical mechanisms: Matrix/M-theory compactification on noncommutative tori, reduction to D-branes in background B-fields, large C-field M5 limits, or quotient/orbifold source links. The result is a topological charge formula, not a derivation of the full M5-brane dynamics or of the complete M-theory action.
ER -