Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data

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 ${\varphi }^4$ theory, and Yukawa theory.

139+61 pages, 26 figures; references and small clarifications added; minor typos corrected, discussion of LC and ET quantization expanded

References in corpus (43)

• Applied Conformal Field Theory
• Nonperturbative Light-Front QCD
• Notes On Higher Spin Symmetries
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter
• A Cheap Alternative to the Lattice?
• $1+1$-Dimensional Large $N$ QCD coupled to Adjoint Fermions
• Two Dimensional QCD coupled to Adjoint Matter and String Theory
• A scaling theory for the long-range to short-range crossover and an infrared duality
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions II. The Z_2-Broken Phase and the Chang Duality
• Hamiltonian truncation approach to quenches in the Ising field theory
• Compactification in the Lightlike Limit
• Glueball spectrum in a (1+1)-dimensional model for QCD
• Matrix product states and variational methods applied to critical quantum field theory
• Orthogonal polynomials of several variables
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• Spontaneous Symmetry Breaking at Infinite Momentum without P+ Zero-Modes
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Nonperturbative light-front Hamiltonian methods
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• A Conformal Truncation Framework for Infinite-Volume Dynamics
• Quench dynamics of the Ising field theory in a magnetic field
• The diagonalization of quantum field Hamiltonians
• Monte Carlo determination of the critical coupling in ${\varphi }_2^4$ theory
• Exploring Hamiltonian Truncation in $\mathbf{d}=2+1$
• Two-dimensional light-front ${\varphi }^4$ theory in a symmetric polynomial basis
• Introduction to stochastic error correction methods
• Broken Chiral Symmetry on a Null Plane
• Zero-Mode Problem on the Light Front
• A 2d (0,2) appetizer
• The non-triviality of the vacuum in light-front quantization: An elementary treatment
• A solution of 2D QCD at Finite $N$ using a conformal basis
• The Light-Front Vacuum
• Light-cone zero modes revisited
• Conformal-helicity duality & the Hilbert space of free CFTs
• Much ado about nothing: vacuum and renormalization on the light-front
• RG flows on $S^d$ and Hamiltonian truncation
• Trialities of minimally supersymmetric 2d gauge theories
• Counterterms in Truncated Conformal Perturbation Theory
• On The S-Matrix of Ising Field Theory in Two Dimensions
• Solving the 2D SUSY Gross-Neveu-Yukawa Model with Conformal Truncation

Cited by in corpus (15)

• Single-particle digitization strategy for quantum computation of a ${\varphi }^4$ scalar field theory
• Matrix Model simulations using Quantum Computing, Deep Learning, and Lattice Monte Carlo
• Exact Symmetries and Threshold States in Two-Dimensional Models for QCD
• Hamiltonian Truncation Effective Theory
• False vacuum decay in the 1+1 dimensional ${\phi }^4$ theory
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Hamiltonian Truncation Crafted for UV-divergent QFTs
• Spinors and conformal correlators
• Lightcone Hamiltonian for Ising Field Theory I: T < T_c
• Critical Coupling for Two-dimensional ${\varphi }^4$ Theory in Discretized Light-Cone Quantization
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation
• Radial Lattice Quantization of 3D ${\varphi }^4$ Field Theory
• Chiral Limit of 2d QCD Revisited with Lightcone Conformal Truncation