Lightcone Effective Hamiltonians and RG Flows

TL;DR

This paper introduces a new prescription for effective lightcone Hamiltonians that incorporate zero mode effects, resolving key issues in LC quantization of deformed CFTs and simplifying Hamiltonian truncation methods.

Contribution

It provides a novel prescription for LC Hamiltonians that addresses zero mode effects and improves the consistency of LC quantization in large N CFTs.

Findings

Resolves non-renormalization issues of the vacuum in LC quantization.

Aligns critical bare parameters between equal-time and LC quantization.

Simplifies Hamiltonian truncation in large N CFTs with AdS duals.

Abstract

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.