Torsion in cohomology and dimensional reduction
| Autor: | Casas, Gonzalo F., Marchesano, Fernando, Zatti, Matteo |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | Conventional wisdom dictates that $\mathbb{Z}_N$ factors in the integral cohomology group $H^p(X_n, \mathbb{Z})$ of a compact manifold $X_n$ cannot be computed via smooth $p$-forms. We revisit this lore in light of the dimensional reduction of string theory on $X_n$, endowed with a $G$-structure metric that leads to a supersymmetric EFT. If massive $p$-form eigenmodes of the Laplacian enter the EFT, then torsion cycles coupling to them will have a non-trivial smeared delta form, that is an EFT long-wavelength description of $p$-form currents of the $(n-p)$-cycles of $X_n$. We conjecture that, whenever torsion cycles are calibrated, their linking number can be computed via their smeared delta forms. From the EFT viewpoint, a torsion factor in cohomology corresponds to a $\mathbb{Z}_N$ gauge symmetry realised by a St\"uckelberg-like action, and calibrated torsion cycles to BPS objects that source the massive fields involved in it. Comment: 44 pages + appendices. V2: References added. Domain wall solution in section 4 reinterpreted |
| Databáze: | arXiv |
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