Anomaly (physics)
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In physics, an anomaly is a classical symmetry—i.e. a symmetry of the Lagrangian—that is broken by quantum effects, usually in quantum field theories. Anomalies in gauge theories have important connections to topology and geometry.
Although anomalies can be considered a short-distance, ultraviolet effect—because they arise because some UV divergent integrals cannot be regularized in such a way that all the symmetries are preserved simultaneously—they are also an infrared (IR) effect because the character of these divergences is determined purely by the long-distance (low-energy) physics (massless particles and fields).
In the Standard Model, the gauge anomalies cancel—and they only cancel once both quarks as well as leptons are included.
The anomalies in gauge symmetries must be cancelled—the total anomaly must vanish—if the theory is consistent. The proof of anomaly cancellation in type I string theory (using the Green-Schwarz mechanism) sparked the first superstring revolution in string theory.
The anomalies in global symmetries do not make the theory inconsistent, but they have important physical consequences.