Two Dimensional Conformal Field Theory from Soft Quantum Electrodynamics in Four Dimensions

TL;DR

This paper develops a two-dimensional conformal field theory effective action for soft modes in 4D QED, connecting IR sector boundary conditions, Ward identities, and conformal properties, including central charge calculation.

Contribution

It introduces an effective conformal field theory framework for soft modes in 4D QED, linking boundary conditions, Ward identities, and IR sector analysis.

Findings

Derived the effective action for soft modes in 4D QED

Calculated the central charge of the conformal theory

Provided boundary conditions and counter-terms for IR sector

Abstract

In this work, we propose an effective action of the two-dimensional conformal field theory for the Soft modes appearing in Quantum ElectroDynamics (QED) in 4 dimensions. This is motivated in two ways. First, we motivate the notion of an effective action for the Soft modes using the path integral formalism. Second, by noting the transformations of the on-shell gauge-fixed QED action, we deduce necessary boundary conditions and the corresponding form of the counter-terms that govern the IR sector. We review a derivation of the Soft Ward-Takahashi identity using path integral methods and offer an alternative derivation that follows from the large-gauge variations of the QED action. Because our effective action is that of a conformal theory, we calculate the relevant central charge.