Abstract
We initiate the application of Hamiltonian Truncation methods to solve strongly coupled QFTs in $d=2+1$. By analysing perturbation theory with a Hamiltonian Truncation regulator, we pinpoint the challenges of such an approach and propose a way that these can be addressed. This enables us to formulate Hamiltonian Truncation theory for $\phi^4$ in $d=2+1$, and to study its spectrum at weak and strong coupling. The results obtained agree well with the predictions of a weak/strong self-duality possessed by the theory. The $\phi^4$ interaction is a strongly relevant UV divergent perturbation, and represents a case study of a more general scenario. Thus, the approach developed should be applicable to many other QFTs of interest.
Highlights
There is currently no known universal and efficient method to derive the phenomenological implications of strongly coupled quantum field theories (QFTs)
We initiate the application of Hamiltonian truncation methods to solve strongly coupled QFTs in d 1⁄4 2 þ 1
Disconnected vacuum diagrams cancel in an intricate manner in Hamiltonian perturbation theory; and we find that such cancelation is spoiled with the ET regularization, introducing new UV divergences
Summary
There is currently no known universal and efficient method to derive the phenomenological implications of strongly coupled quantum field theories (QFTs). A closely related version, coined conformal truncation, exploits light-cone quantization to truncate the wave-functions at infinite volume [3,4,5,6,7] Another guise of HT uses a massive Fock-Space basis to truncate the Hamiltonian. Many of the techniques that we will develop should be useful for formulating HT in any dimension for theories in which V is a strongly relevant perturbation. The results of Hamiltonian truncation at weak coupling must match those of perturbation theory. Disconnected vacuum diagrams cancel in an intricate manner in Hamiltonian perturbation theory; and we find that such cancelation is spoiled with the ET regularization, introducing new UV divergences.
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