[Paper Review] Non-BPS domain wall configurations in a supersymmetric model

Vakhid A. Gani, A. E. Kudryavtsev|arXiv (Cornell University)|Dec 22, 1999

Quantum chaos and dynamical systems4 citations

TL;DR

This paper investigates non-BPS domain wall collisions in a supersymmetric field model using numerical simulations, revealing a critical initial velocity $v_{\text{cr}} \approx 0.9120$ that separates two distinct dynamical regimes: reflection without vacuum state change at $v_i < v_{\text{cr}}$, and vacuum state sequence change at $v_i > v_{\text{cr}}$. The results are consistent with potential-energy analysis.

ABSTRACT

We study the time evolution of configurations in the form of two parallel domain walls moving towards each other in a supersymmetric field model. The configurations involved are not BPS-saturated. It is found that for such collisions there exists some critical value $v_{cr}\approx0.9120$ of the initial velocity v_i of the walls. At v_iv_{cr} the sequence of vacuum states changes. The results of the numerical simulations are in agreement with "potential" consideration.

Motivation & Objective

• To understand the dynamics of non-BPS domain wall configurations in a supersymmetric field model.
• To investigate the outcome of head-on collisions between two parallel domain walls that are not BPS-saturated.
• To determine whether the collision leads to vacuum state transitions or reflection without such transitions.
• To identify a critical initial velocity that separates qualitatively different collision outcomes.

Proposed method

• Numerical simulations were performed to study the time evolution of two parallel domain walls approaching each other.
• The model is a supersymmetric field theory with a scalar potential supporting multiple vacua.
• The initial configuration consists of two domain walls with specified initial velocity $v_i$.
• The evolution is tracked by solving the classical field equations numerically in a 1+1 dimensional spacetime.
• The behavior is analyzed by monitoring the vacuum state sequence and the final configuration after collision.
• Results are compared with predictions from a potential-energy consideration to validate the numerical findings.

Experimental results

Research questions

• RQ1 What happens when two non-BPS domain walls collide at different initial velocities in a supersymmetric model?
• RQ2 Is there a critical velocity above which the vacuum state sequence changes after collision?
• RQ3 Does reflection occur without vacuum state transition for low initial velocities?
• RQ4 How does the potential-energy landscape influence the collision dynamics of non-BPS domain walls?
• RQ5 To what extent do numerical simulations confirm the qualitative predictions from potential-energy arguments?

Key findings

• A critical initial velocity $v_{\text{cr}} \approx 0.9120$ separates two distinct collision outcomes.
• For initial velocities below $v_{\text{cr}}$, the domain walls reflect without changing the sequence of vacuum states.
• For initial velocities above $v_{\text{cr}}$, the sequence of vacuum states changes after collision.
• The numerical results are in agreement with predictions derived from potential-energy analysis.
• The system exhibits a phase transition-like behavior in collision dynamics at the critical velocity.
• The findings demonstrate that non-BPS domain wall collisions in this model are sensitive to initial kinetic energy, with a sharp threshold for topological transition.