Conformal Symmetry - Uses

Uses

The largest possible (global) symmetry group of a non-supersymmetric interacting field theory is a direct product of the conformal group with an internal group. Such theories are known as conformal field theories.

One particular application is to critical phenomena (phase transitions of the second order) in systems with local interactions. The fluctuations in such systems are conformally invariant at the critical point. That allows for classification of universality classes of phase transitions in terms of conformal field theories. Conformal invariance is also discovered in two-dimensional turbulence at high Reynolds number.

Several spaces and theories in high-energy physics admit the conformal symmetry:

• N = 4 supersymmetric Yang-Mills.
• The theory over the worldsheet in string theory.