Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data

TL;DR

This paper introduces and enhances the lightcone conformal truncation (LCT) method for calculating dynamical quantities in 2D quantum field theories, providing new techniques, practical tools, and applications to various models.

Contribution

It develops new CFT radial quantization techniques and SUSY-inspired methods to improve LCT efficiency and applicability, along with comprehensive computational resources.

Findings

Effective LCT implementation for 2D QFTs demonstrated

New techniques improve computational efficiency and symmetry preservation

Application to models like QCD, scalar, and Yukawa theories

Abstract

We both review and augment the lightcone conformal truncation (LCT) method. LCT is a Hamiltonian truncation method for calculating dynamical quantities in QFT in infinite volume. This document is a self-contained, pedagogical introduction and "how-to" manual for LCT. We focus on 2D QFTs which have UV descriptions as free CFTs containing scalars, fermions, and gauge fields, providing a rich starting arena for LCT applications. Along our way, we develop several new techniques and innovations that greatly enhance the efficiency and applicability of LCT. These include the development of CFT radial quantization methods for computing Hamiltonian matrix elements and a new SUSY-inspired way of avoiding state-dependent counterterms and maintaining chiral symmetry. We walk readers through the construction of their own basic LCT code, sufficient for small truncation cutoffs. We also provide a more sophisticated and comprehensive set of Mathematica packages and demonstrations that can be used to study a variety of 2D models. We guide the reader through these packages with several examples and illustrate how to obtain QFT observables, such as spectral densities and the Zamolodchikov $C$-function. Specific models considered are finite $N_c$ QCD, scalar $\phi^4$ theory, and Yukawa theory.