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vorker
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- TL;DR Summary
- Can a DBI-type term stabilize vortons in SU(N) gauge theory? The curvature-dependent energy appears to balance line tension at a specific radius. Looking for feedback on whether this mechanism is physically sound.
I've been studying vortex solutions in SU(N) gauge theories with adjoint scalars. The standard problem is that vortons (closed vortex loops) are unstable and collapse due to line tension. However, I've found that including a DBI-type term (similar to those in string theory effective actions) might provide a stabilization mechanism.
The key point: the DBI term contributes an energy that depends on the extrinsic curvature K of the loop. For a circular vorton of radius R, the total energy becomes:
##E(R) = 2\pi R \mu + \frac{2\pi R}{\Lambda^4}\left[\sqrt{1 + \frac{\Lambda^4}{R^2}} - 1\right]##
where μ is the vortex tension and Λ is the DBI scale. The first term wants to shrink the loop, while the second term diverges as R→0.
Minimizing this gives an equilibrium radius:
##R_{eq} = \frac{\Lambda}{\sqrt{\mu \Lambda^4 - 1}}##
This exists when μ > Λ^(-4), suggesting a parameter regime where vortons are stable.
Has anyone encountered similar stabilization mechanisms for topological defects? Are there known issues with applying DBI terms in this context? Any relevant references would be helpful.
The key point: the DBI term contributes an energy that depends on the extrinsic curvature K of the loop. For a circular vorton of radius R, the total energy becomes:
##E(R) = 2\pi R \mu + \frac{2\pi R}{\Lambda^4}\left[\sqrt{1 + \frac{\Lambda^4}{R^2}} - 1\right]##
where μ is the vortex tension and Λ is the DBI scale. The first term wants to shrink the loop, while the second term diverges as R→0.
Minimizing this gives an equilibrium radius:
##R_{eq} = \frac{\Lambda}{\sqrt{\mu \Lambda^4 - 1}}##
This exists when μ > Λ^(-4), suggesting a parameter regime where vortons are stable.
Has anyone encountered similar stabilization mechanisms for topological defects? Are there known issues with applying DBI terms in this context? Any relevant references would be helpful.
