Lightcone effective Hamiltonians and RG flows

• Published in: The journal of high energy physics Vol. 2018; no. 8; pp. 1 - 52
• Main Authors: Fitzpatrick, A. Liam, Kaplan, Jared, Katz, Emanuel, Vitale, Lorenzo G., Walters, Matthew T.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: Classical and Quantum Gravitation; Conformal Field Theory; Deformation mechanisms; Effective Field Theories; Elementary Particles; High energy physics; Measurement; Nonperturbative Effects; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Renormalization Group; String Theory; Renormalization Group; Effective Field Theories; Conformal Field Theory; Nonperturbative Effects
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2018)120

A bstract We present a prescription for an effective lightcone (LC) Hamiltonian that includes the effects of zero modes, focusing on the case of Conformal Field Theories (CFTs) deformed by relevant operators. We show how the prescription resolves a number of issues with LC quantization, including i) the apparent non-renormalization of the vacuum, ii) discrepancies in critical values of bare parameters in equal-time vs LC quantization, and iii) an inconsistency at large N in CFTs with simple AdS duals. We describe how LC quantization can drastically simplify Hamiltonian truncation methods applied to some large N CFTs, and discuss how the prescription identifies theories where these simplifications occur. We demonstrate and check our prescription in a number of examples.