Singular Pöschl-Teller II potentials and gravitating kinks

Abstract

We report a two-dimensional (2D) gravitating kink model, for which both the background field equations and the linear perturbation equation are exactly solvable. The background solution describes a sine-Gordon kink that interpolating between two asymptotic AdS2 spaces, and can be regarded as a 2D thick brane world solution. The linear perturbation equation can be recasted into a Schrödinger-like equation with singular Pöschl-Teller II potentials. There is no tachyonic state in the spectrum, so the solution is stable against the linear perturbations. Besides, there can be n = 0, 1, 2,⋯ bounded vibrational modes around the kink. The number of these vibrational modes varies with model parameters.

A reduced inner product for kink states

“…Given a stationary kink solution, one may compute its normal modes and even their interactions [31]. Every year, this is done for new classes of models [32][33][34], including recently even gravitating kinks [35,36]. With these normal modes in hand, one can construct the quantum states corresponding to kinks.…”