View source for Modular invariance

In [[Physics:Theoretical physics|theoretical physics]], '''modular invariance''' is the invariance under the [[Group (mathematics)|group]] such as SL(2,Z) of [[Physics:Large diffeomorphism|large diffeomorphism]]s of the [[Torus|torus]]. The name comes from the classical name [[Modular group|modular group]] of this group, as in [[Modular form|modular form]] theory.

In [[Physics:String theory|string theory]], modular invariance is an additional requirement for one-loop diagrams. This helps in getting rid of some [[Physics:Global anomaly|global anomalies]] such as the [[Physics:Gravitational anomaly|gravitational anomalies]]. 

Equivalently, in [[Two-dimensional conformal field theory|two-dimensional conformal field theory]] the torus partition function must be invariant under the modular group SL(2,Z). 
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[[Category:Symmetry]]



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