Modular invariance

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In theoretical physics, modular invariance is the invariance under the group such as SL(2,Z) of large diffeomorphisms of the torus. The name comes from the classical name modular group of this group, as in modular form theory.

In string theory, modular invariance is an additional requirement for one-loop diagrams that some global anomalies, namely the gravitational anomalies, do not appear.