Abstract
We use Lightcone Conformal Truncation (LCT)—a version of Hamiltonian truncation — to study the nonperturbative, real-time dynamics of ϕ4-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 state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d ϕ4-theory in lightcone quantization. We then use LCT with this counterterm prescription to study ϕ4-theory, focusing on the ℤ2 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.
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Anand, N., Katz, E., Khandker, Z.U. et al. Nonperturbative dynamics of (2+1)d ϕ4-theory from Hamiltonian truncation. J. High Energ. Phys. 2021, 190 (2021). https://doi.org/10.1007/JHEP05(2021)190
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DOI: https://doi.org/10.1007/JHEP05(2021)190