Gravitational anomalies

Luis Alvarez-Gaumé, Edward Witten

Research output: Contribution to journalArticlepeer-review

1431 Scopus citations


It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of spin- 1 2 or -3 2 or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.

Original languageEnglish (US)
Pages (from-to)269-330
Number of pages62
JournalNuclear Physics, Section B
Issue number2
StatePublished - Apr 2 1984

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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