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arXiv · 2412.16053

Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space

Niklas Zorbach·Adrian Koenigstein·Jens Braun
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Abstract

Within the Functional Renormalisation Group (FRG) approach, we present a fluid-dynamical approach to solving flow equations for models living in a multi-dimensional 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 (CFD). We demonstrate the effectiveness of our approach by performing explicit benchmark tests using zero-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.

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Niklas Zorbach, Adrian Koenigstein, Jens Braun. 2024-12-20. Functional Renormalization Group meets Computational Fluid Dynamics: RG flows in a multi-dimensional field space. https://arxiv.org/abs/2412.16053

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