Functional Renormalization and $\overline{\text{MS}}$

Understand

Working with scalar field theories, we discuss choices of regulator that, inserted in the functional renormalization group equation, reproduce the results of dimensional regularization at one and two loops.

• The resulting flow equations can be seen as nonperturbative extensions of the $\overline{\text{MS}}\,$ scheme.
• We support this claim by recovering all the multicritical models in two dimensions.
• We discuss a possible generalization to any dimension.