Sphaleron glueballs in NBI theory with symmetrized trace

TL;DR

This paper derives a closed-form SU(2) Born-Infeld action with symmetrized trace for static magnetic configurations, and investigates glueball solutions and black holes in this framework, comparing them with previous models.

Contribution

It provides a new explicit expression for the symmetrized trace NBI action and analyzes glueball solutions and black holes within this model, highlighting their similarities to prior models with different traces.

Findings

Glueball solutions persist with symmetrized trace NBI lagrangian.

Qualitative features of glueballs are similar across models.

Gravity reduces differences between solutions in different models.

Abstract

We derive a closed expression for the SU(2) Born-Infeld action with the symmetrized trace for static spherically symmetric purely magnetic configurations. The lagrangian is obtained in terms of elementary functions. Using it, we investigate glueball solutions to the flat space NBI theory and their self-gravitating counterparts. Such solutions, found previously in the NBI model with the 'square root - ordinary trace' lagrangian, are shown to persist in the theory with the symmetrized trace lagrangian as well. Although the symmetrized trace NBI equations differ substantially from those of the theory with the ordinary trace, a qualitative picture of glueballs remains essentially the same. Gravity further reduces the difference between solutions in these two models, and, for sufficiently large values of the effective gravitational coupling, solutions tends to the same limiting form. The black holes in the NBI theory with the symmetrized trace are also discussed.