Evidence for the unbinding of the 𝜙4 kink’s shape mode

Abstract

The 𝜙4 double-well theory admits a kink solution, whose rich phenomenology is strongly affected by the existence of a single bound excitation called the shape mode. We find that the leading quantum correction to the energy needed to excite the shape mode is −0.115567λ/M in terms of the coupling λ/4 and the meson mass M evaluated at the minimum of the potential. On the other hand, the correction to the continuum threshold is −0.433λ/M. A naive extrapolation to finite coupling then suggests that the shape mode melts into the continuum at the modest coupling of λ/4 ∼ 0.106M2, where the ℤ2 symmetry is still broken.

Removing tadpoles in a soliton sector

“…In refs. [4,5] it was shown that the same is true of the energies of excited states. These tadpoles do not lead to any inconsistencies.…”

Singular Pöschl-Teller II potentials and gravitating kinks

“…For example, the linear perturbations around the sine-Gordon kink and the φ 4 kink in flat space satisfy Schrödinger-like equations with V PT,− (x; 1, 0) and V PT,− (x; 2, 0), respectively [14][15][16]. The solvability of these potentials makes it possible to give some quantitative discussions on the quantization [3,[14][15][16][17][18] and dynamical collision phenomena of kinks [19][20][21][22][23][24][25][26], see [27] for a comprehensive review. Perturbation equations of some de Sitter thick branes [28][29][30] or black holes solutions [31][32][33][34][35][36][37] are also closely related to the regular PT II potentials.…”

Spectral Walls at One Loop

“…In this approach, the quantum field is expanded about a classical solution at a fixed base point in moduli space. Besides being manifestly UV finite, the main advantage is that the treatment is fully linear, allowing access to problems [21,22] which would be prohibitively difficult with traditional methods. The limitation is that it can only treat kinks near a base point, which is arbitrary but fixed in each calculation.…”