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Physical review. D/Physical review. D.

Optimization and stabilization of functional renormalization group flows

Niklas Zorbach, Jonas Stoll, Jens Braun

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.15120/gsi-2026-00473

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We investigate functional renormalization group structure of closure-consistent relational transport field theories. Building on closure spectral stability and renormalization flow analysis, we construct closure-consistent functional renormalization group equations governing scale evolution of closure-consistent effective transport configuration functionals. We analyze closure spectral operator flow under functional renormalization and derive structural conditions under which closure spectral persistence may remain stable under full functional RG evolution. Using closure-consistent truncation schemes and toy functional RG closure models, we demonstrate how closure spectral structure may constrain effective transport sector evolution across scales. While not providing a complete nonperturbative closure-consistent quantum field theory, the present work establishes a framework for analyzing closure spectral persistence under functional renormalization and provides a basis for investigating closure-consistent transport sector stability in fully interacting quantum field regimes.
We investigate functional renormalization group structure of closure-consistent relational transport field theories. Building on closure spectral stability and renormalization flow analysis,we construct closure-consistent functional renormalization group equations governing scale evolution of closure-consistent effective transport configuration functionals. We analyze closure spectral operator flow under functional renormalization and derive structural conditions underwhich closure spectral persistence may remain stable under full functional RG evolution. Using closure-consistent truncation schemes and toy functional RG closure models, we demonstratehow closure spectral structure may constrain effective transport sector evolution across scales.While not providing a complete nonperturbative closure-consistent quantum field theory, thepresent work establishes a framework for analyzing closure spectral persistence underfunctional renormalization and provides a basis for investigating closure-consistent transportsector stability in fully interacting quantum field regimes.
We construct a family of holomorphic -functions whose renormalization group (RG) flow preserves the (2) modular symmetry and reproduces the observed stability of the Hall plateaus. The semicircle law relating the longitudinal and Hall conductivities that has been experimentally observed is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependence of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occurring in the crossover of the permitted transitions is discussed.