A transition in the spectrum of the topological sector of $\phi_2^4$ theory at strong coupling

TL;DR

This paper studies the transition in the spectrum of the topological sector of 2D $\

Contribution

It reveals a transition from kink to kink-antikink-kink configurations at strong coupling, indicating kink condensation as the mechanism for phase transition.

Findings

Identification of a critical coupling for the topological transition.

Observation of a kink-antikink-kink structure in low-lying states.

Evidence of kink condensation driving symmetry restoration.

Abstract

We investigate the strong coupling region of the topological sector of the two-dimensional $\phi^4$ theory. Using discrete light cone quantization (DLCQ), we extract the masses of the lowest few excitations and observe level crossings. To understand this phenomena, we evaluate the expectation value of the integral of the normal ordered $\phi^2$ operator and we extract the number density of constituents in these states. A coherent state variational calculation confirms that the number density for low-lying states above the transition coupling is dominantly that of a kink-antikink-kink state. The Fourier transform of the form factor of the lowest excitation is extracted which reveals a structure close to a kink-antikink-kink profile. Thus, we demonstrate that the structure of the lowest excitations becomes that of a kink-antikink-kink configuration at moderately strong coupling. We extract the critical coupling for the transition of the lowest state from that of a kink to a kink-antikink-kink. We interpret the transition as evidence for the onset of kink condensation which is believed to be the physical mechanism for the symmetry restoring phase transition in two-dimensional $\phi^4$ theory.