Minimal Model Renormalization Group Flows: Noninvertible Symmetries and Nonperturbative Description.

Area of Science:

• Theoretical Physics
• Quantum Field Theory
• String Theory

Background:

• Investigates renormalization group (RG) flows between Virasoro minimal models.
• Focuses on two-dimensional conformal field theories (2D CFTs) protected by noninvertible symmetries.
• Extends previous studies on Z_{2}-symmetric flows.

Purpose of the Study:

• To systematically map the space of RG flows beyond Z_{2}-symmetric cases.
• To introduce a method for calculating exact finite-size, ground-state energies for these flows.
• To explore the interplay between exact solvability and noninvertible symmetries.

Main Methods:

• Employs anomaly matching conditions to identify and characterize RG flows.
• Introduces a family of nonlinear integral equations (NLIEs).
• Applies NLIEs to calculate ground-state energies for both integrable and nonintegrable flows.

Main Results:

• Successfully maps RG flows between minimal models, including non-integrable cases like M(kq+I,q)→M(kq-I,q).
• The derived NLIEs generalize known integrable flows (e.g., ϕ_{(1,3)}, ϕ_{(1,5)}, ϕ_{(1,2)}, ϕ_{(2,1)}).
• Provides a nonperturbative description and a test for flows predicted by anomaly matching.

Conclusions:

• Uncovers a novel connection between exact solvability and noninvertible symmetries in 2D CFTs.
• The developed NLIE framework offers a powerful tool for studying complex RG flows.
• This work validates conjectured RG flows and opens new avenues for theoretical physics research.