Nonperturbative renormalization group in a light-front three-dimensional real scalar model

TL;DR

This paper applies a nonperturbative renormalization group approach to a three-dimensional real scalar model with spontaneous symmetry breaking, using Hamiltonian diagonalization and Fock space truncation to analyze critical behavior.

Contribution

It introduces a nonperturbative renormalization method for the 3D scalar model using Tamm-Dancoff truncation and Hamiltonian diagonalization, providing insights into the critical line and symmetry breaking.

Findings

Critical line calculated via Hamiltonian diagonalization.

Weak dependence of the critical line on the $\

Field shift determined to ensure ground state mass vanishes.

Abstract

The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. The marginal ($\phi^6$) coupling dependence of the critical line is weak. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as $\phi(x)\to\varphi(x)+v$. The shifted value $v$ is determined as a function of running mass and coupling so that the mass of the ground state vanishes.