Citation

BibTex format

@article{Borsten:2021:10.1007/JHEP12(2021)178,
author = {Borsten, L and Duff, MJ and Nagy, S},
doi = {10.1007/JHEP12(2021)178},
journal = {The Journal of High Energy Physics},
title = {Odd dimensional analogue of the Euler characteristic},
url = {http://dx.doi.org/10.1007/JHEP12(2021)178},
volume = {2021},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - When compact manifolds X and Y are both even dimensional, their Euler characteristics obey the Künneth formula χ(X × Y) = χ(X)χ(Y). In terms of the Betti numbers bp(X), χ(X) = Σp(−1)pbp(X), implying that χ(X) = 0 when X is odd dimensional. We seek a linear combination of Betti numbers, called ρ, that obeys an analogous formula ρ(X × Y) = χ(X)ρ(Y) when Y is odd dimensional. The unique solution is ρ(Y) = − Σp(−1)ppbp(Y). Physical applications include: (1) ρ → (−1)mρ under a generalized mirror map in d = 2m + 1 dimensions, in analogy with χ → (−1)mχ in d = 2m; (2) ρ appears naturally in compactifications of M-theory. For example, the 4-dimensional Weyl anomaly for M-theory on X4 × Y7 is given by χ(X4)ρ(Y7) = ρ(X4 × Y7) and hence vanishes when Y7 is self-mirror. Since, in particular, ρ(Y × S1) = χ(Y), this is consistent with the corresponding anomaly for Type IIA on X4 × Y6, given by χ(X4)χ(Y6) = χ(X4 × Y6), which vanishes when Y6 is self-mirror; (3) In the partition function of p-form gauge fields, ρ appears in odd dimensions as χ does in even.
AU  - Borsten,L
AU  - Duff,MJ
AU  - Nagy,S
DO  - 10.1007/JHEP12(2021)178
PY  - 2021///
SN  - 1029-8479
TI  - Odd dimensional analogue of the Euler characteristic
T2  - The Journal of High Energy Physics
UR  - http://dx.doi.org/10.1007/JHEP12(2021)178
UR  - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000734916700002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=a2bf6146997ec60c407a63945d4e92bb
UR  - https://link.springer.com/article/10.1007/JHEP12(2021)178
UR  - http://hdl.handle.net/10044/1/106914
VL  - 2021
ER  -
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