A Conformal Truncation Framework for Infinite-Volume Dynamics

Abstract

We present a new framework for studying conformal field theories deformed by one or more relevant operators. The original CFT is described in infinite volume using a basis of states with definite momentum, $P$, and conformal Casimir, $\mathcal{C}$. The relevant deformation is then considered using lightcone quantization, with the resulting Hamiltonian expressed in terms of this CFT basis. Truncating to states with $\mathcal{C}\le {\mathcal{C}}_{\max }$, one can numerically find the resulting spectrum, as well as other dynamical quantities, such as spectral densities of operators. This method requires the introduction of an appropriate regulator, which can be chosen to preserve the conformal structure of the basis. We check this framework in three dimensions for various perturbative deformations of a free scalar CFT, and for the case of a free $O(N)$ CFT deformed by a mass term and a non-perturbative quartic interaction at large-$N$. In all cases, the truncation scheme correctly reproduces known analytic results. We also discuss a general procedure for generating a basis of Casimir eigenstates for a free CFT in any number of dimensions.

48+37 pages, 17 figures; v2: references added, small clarifications

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Cited by in corpus (35)

• Operator bases, $S$-matrices, and their partition functions
• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Momentum-space conformal blocks on the light cone
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Quantum simulation of quantum field theories as quantum chemistry
• Conformal 3-point functions and the Lorentzian OPE in momentum space
• Momentum space parity-odd CFT 3-point functions
• RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model
• Exploring Hamiltonian Truncation in $\mathbf{d}=2+1$
• Lightcone Effective Hamiltonians and RG Flows
• Thermalization and chaos in a 1+1d QFT
• Convergent Momentum-Space OPE and Bootstrap Equations in Conformal Field Theory
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Hamiltonian truncation in Anti-de Sitter spacetime
• Graviton Scattering and a Sum Rule for the c Anomaly in 4D CFT
• Hamiltonian Truncation Effective Theory
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• False vacuum decay in the 1+1 dimensional ${\phi }^4$ theory
• Chirally Factorised Truncated Conformal Space Approach
• Quantum quenches in an interacting field theory: full quantum evolution vs. semi-classical approximations
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• Conformal Truncation of Chern-Simons Theory at Large $N_f$
• Towards a nonperturbative construction of the $S$-matrix
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• RG flows on $S^d$ and Hamiltonian truncation
• ANEC in $\lambda {\varphi }^4$ theory
• Spinors and conformal correlators
• Sine-Gordon model at finite temperature: the method of random surfaces
• On computing non-equilibrium dynamics following a quench
• A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation