What question did this study set out to answer?

The aim is to construct and analyze the Hybrid Renormalization Group flow related to gauge theory and mass gaps.

January 25, 20260 citationsOpen Access

Global Stability of the Hybrid Balaban–Brydges Flow for a Magnetically Charged Gas: Connecting the UV Lattice Gauge Theory to the IR Semiclassical Mass Gap

Key Points

The aim is to construct and analyze the Hybrid Renormalization Group flow related to gauge theory and mass gaps.
Rigorous construction of Hybrid Renormalization Group flow
Utilization of Balaban’s Block Axial Gauge for stability
Demonstration of the Matching Lemma for effective action convergence
Application of polymer expansion in bion gas analysis
Proven ultraviolet stability of the theory with respect to locality and gauge invariance
Effective action meets Kotecký-Preiss convergence condition at transition scale
Dynamical flow of effective mass parameter with a positive global attractor
Existence of mass gap in continuum limit established

Abstract

AbstractThis paper details the rigorous construction of the Hybrid Renormalization Group flow utilized in the Constructive Gauge Theory Program (CGTP). We demonstrate the ultraviolet stability of the theory employing Balaban’s Block Axial Gauge, which preserves locality while controlling gauge invariance during the block‑spin transformations. Crucially, we prove a “Matching Lemma” which guarantees that the effective action at the transition scale satisfies the Kotecký–Preiss convergence condition required for the infrared Phase II. Finally, utilizing a polymer expansion for the bion gas, we demonstrate that the effective mass parameter follows a dynamical flow with a strictly positive global attractor, ensuring the existence of the mass gap in the continuum limit.

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