Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation

Abstract

We use Lightcone Conformal Truncation (LCT) -- a version of Hamiltonian truncation -- to study the nonperturbative, real-time dynamics of ${\varphi }^4$-theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily \emph{state-dependent}, and UV sensitivity cannot be canceled with standard local operator counterterms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d ${\varphi }^4$-theory in lightcone quantization. We then use LCT with this counterterm prescription to study ${\varphi }^4$-theory, focusing on the ${\mathbb{Z}}_2$ symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.

Comments: 33 pages + appendices, 14 figures; references added