Communications in Mathematical Physics

, Volume 100, Issue 2, pp 197–229 | Cite as

Global gravitational anomalies

  • Edward Witten


A general formula for global gauge and gravitational anomalies is derived. It is used to show that the anomaly free supergravity and superstring theories in ten dimensions are all free of global anomalies that might have ruined their consistency. However, it is shown that global anomalies lead to some restrictions on allowed compactifications of these theories. For example, in the case of O(32) superstring theory, it is shown that a global anomaly related to π7(O(32)) leads to a Dirac-like quantization condition for the field strength of the antisymmetric tensor field.

Related to global anomalies is the question of the number of fermion zero modes in an instanton field. It is argued that the relevant gravitational instantons are exotic spheres. It is shown that the number of fermion zero modes in an instanton field is always even in ten dimensional supergravity.


Neural Network Statistical Physic Complex System Field Strength Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Edward Witten
    • 1
  1. 1.Joseph Henry LaboratoriesPrinceton UniversityPrincetonUSA

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