Hamiltonian Truncation with larger dimensions

• Published in: The journal of high energy physics Vol. 2022; no. 5; pp. 151 - 35
• Main Authors: Miró, Joan Elias, Ingoldby, James
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2022; Springer Nature B.V; SpringerOpen
• Subjects: Approximation; Classical and Quantum Gravitation; Elementary Particles; Field Theories in Lower Dimensions; High energy physics; Integrable Field Theories; Perturbation theory; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; Renormalization and Regularization; Scale and Conformal Symmetries; String Theory; Yang-Mills theory; Field Theories in Lower Dimensions; Integrable Field Theories; Scale and Conformal Symmetries; Renormalization and Regularization
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2022)151

A bstract Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension ∆. UV divergences arise when ∆ is larger than half of the spacetime dimension d . These divergences can be regulated by HT or by using a more conventional local regulator. In this work we show that extra UV divergences appear when using HT rather than a local regulator for ∆ ≥ d/ 2 + 1 / 4, revealing a striking breakdown of locality. Our claim is based on the analysis of conformal perturbation theory up to fourth order. As an example we compute the Casimir energy of d = 2 Minimal Models perturbed by operators whose dimensions take values on either side of the threshold d/ 2 + 1 / 4.