Large Momentum EFT and Lightcone Quantization

TL;DR

This paper introduces a novel method for computing the effective action at infinite momentum in 1+1 dimensional quantum field theories, especially applied to the Ising Field Theory, using lightcone quantization without requiring a Lagrangian framework.

Contribution

It develops a Lagrangian-independent approach to derive the effective lightcone Hamiltonian at infinite momentum, validated through numerical comparison with TCSA results.

Findings

The effective Hamiltonian simplifies in the low-temperature phase.

The Hamiltonian depends on volume only via the vacuum expectation value of sigma.

The method is successfully applied to the Ising Field Theory with energy and magnetic deformations.

Abstract

We develop methods for computing the effective action at infinite momentum for $1+1d$ QFTs at finite volume which do not rely on the theory having a Lagrangian description. We do this by taking the infinite momentum limit of equal-time quantization and integrating out all except for the chiral modes of the theory. Our main application of this method is to the Ising Field Theory (IFT), with an energy and magnetic deformation, where we compute the effective lightcone Hamiltonian numerically and check it against results from TCSA. Remarkably, in the low-temperature phase, the Lorentz invariant effective Hamiltonian at infinite momentum takes a very compact form and depends on the volume only through the finite volume vacuum expectation value of $\langle\sigma\rangle$, the spin operator.