Hamiltonian Truncation of Large $N_f$ QED and Large $N$ Vector-like Theories in $d=2+1$

TL;DR

This paper develops an exact Hamiltonian diagonalization method for large N vector-like theories in 2+1 dimensions using lightcone quantization, exemplified by large Nf QED3, enabling computation of spectral and scattering data.

Contribution

It introduces a Hamiltonian approach with lightcone quantization for large N theories, allowing exact solutions and spectral analysis, with potential extensions to finite N.

Findings

Exact diagonalization of Hamiltonian in large N limit

Construction of eigenstates, spectral density, S-matrix, and form factors

Application to large Nf QED3 as a concrete example

Abstract

We consider a general class of large $N$ vector-like theories in $d=2+1$ in a Hamiltonian approach. We show that by using lightcone quantization and the $N\to\infty$ limit, we can diagonalize the Hamiltonian exactly and construct the eigenstates, spectral density, S-matrix, and form factors for the theory. For concreteness, we mainly focus on QED$_3$ at large $N_f$ as an explicit example. We comment on extending the approach to finite $N$ calculations.