Local Anomalies and Local Equivariant Cohomology

被引：0
作者：
Roberto Ferreiro Pérez
机构：
[1] Facultad de Ciencias Económicas y Empresariales,Departamento de Economía Financiera y Contabilidad I
[2] UCM,undefined
来源：
Communications in Mathematical Physics | 2009年 / 286卷
关键词：
Dirac Operator; Cohomology Class; Riemannian Metrics; Equivariant Cohomology; Anomaly Cancellation;
D O I：
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学科分类号：
摘要：
The locality conditions for the vanishing of local anomalies in field theory are shown to admit a geometrical interpretation in terms of local equivariant cohomology. This interpretation allows us to solve the problem proposed by Singer in [31], and consists in defining an adequate notion of local cohomology to deal with the problem of locality in the geometrical approaches to the study of local anomalies based on the Atiyah-Singer index theorem. Moreover, using the relation between local cohomology and the cohomology of jet bundles studied in [19] we obtain necessary and sufficient conditions for the cancellation of local gravitational and mixed anomalies.
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页码：445 / 458
页数：13
相关论文
共 46 条
[1]  
Álvarez O.(1984)Gravitational Anomalies and the Family’s Index Theorem Commun. Math. Phys. 96 409-417
[2]  
Singer I.(1985)The structure of gauge and gravitational anomalies Ann. Phys. 161 423-490
[3]  
Zumino B.(1984)Dirac operators coupled to vector potentials Proc. Natl. Acad. Sci. USA 81 2597-2600
[4]  
Álvarez-Gaumé L.(2000)Local BRST cohomology in gauge theories Phys. Rep. 338 439-569
[5]  
Ginsparg P.(1982)Classes caractéristiques équivariantes. Formules de localisation en cohomologie équivariante C. R. Acad. Sci. Paris 295 539-541
[6]  
Atiyah M.F.(1988)Wess-Zumino Terms and the Geometry of the Determinant Line Bundle Phys. Lett. B 209 503-506
[7]  
Singer I.(1983)Some Remarks on BRS Transformations, Anomalies and the Cohomology of the Lie Algebra of the Group of Gauge Transformations Commun. Math. Phys. 87 589-603
[8]  
Barnich G.(1986)Consistent and covariant anomalies and local cohomology Phys. Rev. D (3) 33 3055-3059
[9]  
Brandt F.(1987)The evaluation map in Field Theory and strings I Commun. Math. Phys. 112 237-282
[10]  
Henneaux M.(2001)The geometry of the bundle of connections Math. Z. 236 797-811
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