Functional renormalization group meets computational fluid dynamics: RG flows in a multidimensional field space

Within the functional renormalization group framework, we present a fluid-dynamical approach to solving flow equations for models living in a multidimensional field space. To this end, the underlying exact flow equation of the effective potential is reformulated as a set of nonlinear advection-diffusion-type equations which can be solved using the Kurganov-Tadmor central scheme, a modern finite-volume discretization from computational fluid dynamics. We demonstrate the effectiveness of our approach by performing explicit benchmark tests using ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:mn>0</a:mn> <a:mo>+</a:mo> <a:mn>0</a:mn> </a:mrow> </a:math> )-dimensional models with two discretized field-space directions or two symmetry invariants. Our techniques can be directly applied to flow equations of effective potentials of general (fermion-)boson systems with multiple invariants or condensates, as we also demonstrate for two concrete examples in three spacetime dimensions.