Odd dimensional analogue of the Euler characteristic

Author:

Borsten L.ORCID,Duff M. J.,Nagy S.

Abstract

Abstract 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.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

Reference70 articles.

1. M. J. Duff and S. Ferrara, Generalized mirror symmetry and trace anomalies, Class. Quant. Grav. 28 (2011) 065005 [arXiv:1009.4439] [INSPIRE].

2. M. J. Duff and S. Ferrara, Four curious supergravities, Phys. Rev. D 83 (2011) 046007 [arXiv:1010.3173] [INSPIRE].

3. M. J. Duff, S. Ferrara and A. Marrani, D = 3 unification of curious supergravities, JHEP 01 (2017) 023 [arXiv:1610.08800] [INSPIRE].

4. M. J. Duff and P. van Nieuwenhuizen, Quantum inequivalence of different field representations, Phys. Lett. B 94 (1980) 179 [INSPIRE].

5. E. Witten, On S duality in Abelian gauge theory, Selecta Math. 1 (1995) 383 [hep-th/9505186] [INSPIRE].

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Tree-level color–kinematics duality implies loop-level color–kinematics duality up to counterterms;Nuclear Physics B;2023-04

2. Massive Ray-Singer torsion and path integrals;Journal of High Energy Physics;2022-08-23

3. Introduction to the special issue dedicated to Michael J. Duff FRS on the occasion of his 70th birthday;Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences;2022-03

4. Topological G2 and Spin(7) strings at 1-loop from double complexes;Journal of High Energy Physics;2022-02

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3