Hamiltonian truncation in Anti-de Sitter spacetime

TL;DR

This paper introduces a Hamiltonian truncation approach to study strongly coupled quantum field theories in two-dimensional Anti-de Sitter spacetime, providing a new computational tool for analyzing their spectra and boundary conditions.

Contribution

It develops a novel Hamiltonian truncation method for QFTs in AdS, including a prescription to handle divergences and numerical tests on various models.

Findings

Finite physical energies obtained through the new prescription.

Numerical results consistent with theoretical expectations.

All conformal boundary conditions are connected via bulk RG flows in AdS.

Abstract

Quantum Field Theories (QFTs) in Anti-de Sitter (AdS) spacetime are often strongly coupled when the radius of AdS is large, and few methods are available to study them. In this work, we develop a Hamiltonian truncation method to compute the energy spectrum of QFTs in two-dimensional AdS. The infinite volume of constant timeslices of AdS leads to divergences in the energy levels. We propose a simple prescription to obtain finite physical energies and test it with numerical diagonalization in several models: the free massive scalar field, $\phi^4$ theory, Lee-Yang and Ising field theory. Along the way, we discuss spontaneous symmetry breaking in AdS and derive a compact formula for perturbation theory in quantum mechanics at arbitrary order. Our results suggest that all conformal boundary conditions for a given theory are connected via bulk renormalization group flows in AdS.