Hamiltonian truncation in Anti-de Sitter spacetime

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, ${\varphi }^4$ 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.

63 pages + appendices, 44 figures

References in corpus (7)

• Writing CFT correlation functions as AdS scattering amplitudes
• Local bulk S-matrix elements and CFT singularities
• TASI lectures on AdS/CFT
• Conformal field theories in anti-de Sitter space
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>T_c. Perturbative analysis

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• Hyperbolic Lattice for Scalar Field Theory in AdS${}_3$
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• Renormalization group flows in AdS and the bootstrap program
• Exploring Confinement in Anti-de Sitter Space
• Demystifying integrable QFTs in AdS: No-go theorems for higher-spin charges
• Finite-coupling spectrum of O(N) model in AdS