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arXiv · 2104.10689

Hamiltonian truncation in Anti-de Sitter spacetime

Matthijs Hogervorst·Marco Meineri·Joao Penedones·Kamran Salehi Vaziri
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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.

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Matthijs Hogervorst, Marco Meineri, Joao Penedones, Kamran Salehi Vaziri. 2021-04-21. Hamiltonian truncation in Anti-de Sitter spacetime. https://doi.org/10.1007/jhep08(2021)063

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