Functional renormalization of N scalars with O(N) invariance

Understand

We discuss general theories of N scalar fields with O(N) symmetry.

• In addition to the standard case of linearly realized symmetry there are also examples that carry nonlinear realizations, with the topology of a cylinder $R\times S^{N-1}$ or a sphere $S^N$.
• We write flow equations for the theory in the second order of the derivative expansion in the background field and discuss the properties of scaling solutions with vanishing potential.