Abstract
Odd dimensional Yang-Mills theories with an extra ‘topological mass” term, defined by the Chern-Simons secondary characteristic, are discussed. It is shown in detail how the topological mass affects the equal time charge commutation relations and how the modified commutation relations are related to non-abelian chiral anomalies in even dimensions. We also study the SU(3) chiral model (Wess-Zumino model) in four dimensions and we show how a gauge invariant interaction with an external SU(3) vector potential can be defined with the help of the Chern-Simons characteristic in five dimensions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jackiw, R., Templeton, S.: How super-renormalizable interaction cure their infrared divergences. Phys. Rev.D23, 2291 (1981); Schonfeld, J.: A mass term for three-dimensional gauge fields. Nucl. Phys.B185, 157 (1981)
Chern, S., Simons, J.: Characteristic forms and geometric invariants. Ann. Math.99, 48 (1974)
Mickelsson, J.: On a relation between massive Yang-Mills theories and dual string models. Lett. Math. Phys.7, 45 (1983)
Wess, J., Zumino, B.: Consequences of anomalous Ward identities. Phys. Lett.37B, 95 (1971)
Zumino, B., Wu Yong-Shi, Zee, A.: Chiral anomalies, higher dimensions and differential geometry. Preprint 40048-18 P3, Berkeley, California (1983)
Jackiw, R.: Topological investigations of quantized gauge theories. Lectures in Les Houches, July–August 1983; MIT-preprint CTP No. 1108 (1983)
Bonora, L., Cotta-Ramusino, P.: Some remarks on BRS transformations, anomalies and the cohomology of the Lie algebra of the group of gauge transformations. Commun. Math. Phys.87, 589 (1983)
Deser, S., Jackiw, R., Templeton, S.: Three-dimensional massive gauge theories. Phys. Rev. Lett.48, 975 (1982); Topologically massive gauge theories. Ann. Phys. (NY)140, 372 (1982)
Witten, E.: Global aspects of current algebra. Preprint, Princeton (1983)
Magnus, W.: On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math.7, 649 (1954)
Cronström, C., Mickelsson, J.: On topological boundary characteristics in nonabelian gauge theory. J. Math. Phys.24, 2528 (1983)
Frampton, P. H., Kephart, T. W.: Analysis of anomalies in higher space-time dimensions. Phys. Rev.D28, 1010 (1983); Frampton, P. H., Kephart, T. W.: Explicit evaluation of anomalies in higher dimensions. Phys. Rev. Lett.50, 1343 (1983); Frampton, P. H., Kephart, T. W.: Consistency conditions for Kaluza-Klein anomalies. Phys. Rev. Lett.50, 1347 (1983)
Faddeev, L. D.: Operator anomaly for the Gauss law. Phys. Lett.145B, 81 (1984)
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
Rights and permissions
About this article
Cite this article
Mickelsson, J. Chiral anomalies in even and odd dimensions. Commun.Math. Phys. 97, 361–370 (1985). https://doi.org/10.1007/BF01213402
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01213402