Physics on and off the light cone

TL;DR

This paper explores the interplay of conformal symmetry and light-front physics, examining how symmetry breaking leads to mass generation and connecting these ideas to various theoretical frameworks like AdS/CFT.

Contribution

It provides a detailed analysis of conformal symmetry on and off the light cone, clarifies the equivalence of different commutator formulations, and links light-front physics to other approaches like the infinite momentum frame.

Findings

Conformal symmetry is the full symmetry on the light cone, not just Lorentz symmetry.

Equal-time and equal light-front-time commutators are equivalent despite apparent differences.

Mass scales can emerge dynamically at a conformal fixed point.

Abstract

We study light-front physics and conformal symmetry, and their interplay both on and off the light cone. The full symmetry of the light cone is conformal symmetry not just Lorentz symmetry. Spontaneously breaking conformal symmetry gives masses to particles and takes them off the light cone. Canonical quantization specifies equal-time commutators on the light cone. Equal instant-time and equal light-front-time commutators look very different, but can be shown to be equivalent by looking at unequal-time commutators. We discuss the connection of the light-front approach to the infinite momentum frame approach, and show that vacuum graphs are outside this framework. We show that there is a light-front structure to both AdS/CFT and the eikonal approximation. While mass generation involves scale breaking mass scales, we show that such mass scales can arise via dynamical symmetry breaking in the presence of scale invariant interactions at a renormalization group fixed point.