Loading…
Torsion in cohomology and dimensional reduction
A bstract Conventional wisdom dictates that ℤ N factors in the integral cohomology group H p ( X n , 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...
Saved in:
Published in: | The journal of high energy physics 2023-09, Vol.2023 (9), p.61-46, Article 61 |
---|---|
Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | A
bstract
Conventional wisdom dictates that ℤ
N
factors in the integral cohomology group
H
p
(
X
n
, 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 ℤ
N
gauge symmetry realised by a Stückelberg-like action, and calibrated torsion cycles to BPS objects that source the massive fields involved in it. |
---|---|
ISSN: | 1029-8479 1029-8479 |
DOI: | 10.1007/JHEP09(2023)061 |