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.
Highlights
Introduction and summaryIn this work, we study the nonperturbative, real-time dynamics of φ4-theory in 2+1 dimensions
Figure 8: we show that higher eigenvalues approach zero consistently with the mass gap and that our state-dependent counterterm is crucial for ensuring that eigenvalue ratios match theoretical predictions as we approach the critical point
As we will discuss below, cL should be greater than some threshold in order for the mass gap to close, and at finite truncation, we find in practice that the IR results converge most quickly for values of cL within a particular range
Summary
We study the nonperturbative, real-time dynamics of φ4-theory in 2+1 dimensions (focusing on the Z2 symmetry-preserving phase). Motivations for working in lightcone quantization is that it allows for LCT to be formulated in infinite volume (at least formally, as we will see), which facilitates the computation of physical observables like correlation functions In this way, LCT provides access to different types of dynamical observables and nicely complements other Hamiltonian truncation methods. Elias-Miró and Hardy presented a solution to state-dependent counterterms for (2+1)d φ4-theory in finite volume within equal-time quantization [34] They were able to use their prescription to compute the spectrum of the theory and check the predictions of a weak/strong-coupling self-duality. Are very general and should be applicable to many other QFTs. We are hopeful that these works will open the door to applying Hamiltonian truncation to many new classes of QFTs. Returning to the model at hand, we use LCT along with our counterterm prescription to study the dynamics of (2+1)d φ4-theory, focusing on the Z2 symmetry-preserving phase.
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