Dynamical Zero Modes and Criticality in Continuous Light Cone Quantization of Phi^{4}_{1+1}

TL;DR

This paper investigates the critical behavior of 2D scalar field theory using continuous light cone quantization, introducing dynamical zero modes that influence the dispersion relation and critical exponents, with exact calculations of the beta function.

Contribution

It introduces the concept of dynamical zero modes in continuous light cone quantization and demonstrates their impact on critical phenomena and the beta function in 2D scalar field theory.

Findings

Dynamical zero modes lead to a non-trivial covariant dispersion relation.

The critical exponent η is governed by conformal transformations in the infinite volume limit.

The beta function is exactly calculated and found to be non-analytic with a critical exponent ω=2.

Abstract

Critical behaviour of the 2D scalar field theory in the LC framework is reviewed. The notion of dynamical zero modes is introduced and shown to lead to a non trivial covariant dispersion relation only for Continuous LC Quantization (CLCQ). The critical exponent $\eta$ is found to be governed by the behaviour of the infinite volume limit under conformal transformations properties preserving the local LC structure. The $\beta$-function is calculated exactly and found non-analytic, with a critical exponent $\omega=2$, in agreement with the conformal field theory analysis of Calabrese et al.