Existence of $U(1)$ Gauged Q-balls for A Field Model with Sixth-order Potential

TL;DR

This paper proves the existence of $U(1)$ gauged Q-balls in a sixth-order potential field theory, using a constrained minimization approach, and explores their qualitative properties.

Contribution

It introduces a new method to establish the existence of gauged Q-balls in complex potentials and analyzes their qualitative features.

Findings

Existence of $U(1)$ gauged Q-balls proven.

Q-balls exhibit monotonicity and boundedness.

Asymptotic behavior characterized.

Abstract

Q-balls are non-topological solitons in a large family of field theories. We focus on the existence of $U(1)$ gauged Q-balls for a field theory with sixth-order potential. The problem can be reduced to proving the existence of critical points for some indefinite functional. For this, we use a constrained minimization approach to obtain the existence of critical points. Moreover, we establish some qualitative properties of the Q-ball solution, such as monotonicity, boundedness and asymptotic behavior.