From Here to Criticality: Renormalization Group Flow Between Two Conformal Field Theories

TL;DR

This paper nonperturbatively studies the renormalization group flow between two conformal field theories, computing correlation functions and key parameters to understand the transition from the A3 to A2 models.

Contribution

It provides a numerical analysis of the RG flow between two specific superconformal minimal models, including correlation functions and operator data, with a review of related geometric QFT aspects.

Findings

Correlation functions match expected asymptotic behavior

Infrared theory characterized by specific central charge and OPE coefficients

Excellent agreement between numerical results and theoretical predictions

Abstract

Using nonperturbative techniques, we study the renormalization group trajectory between two conformal field theories. Specifically, we investigate a perturbation of the A3 superconformal minimal model such that in the infrared limit the theory flows to the A2 model. The correlation functions in the topological sector of the theory are computed numerically along the trajectory, and these results are compared to the expected asymptotic behavior. Excellent agreement is found, and the characteristic features of the infrared theory, including the central charge and the normalized operator product expansion coefficients are obtained. We also review and discuss some aspects of the geometrical description of N=2 supersymmetric quantum field theories recently uncovered by S. Cecotti and C. Vafa.