Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations

Details Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations Self-similarity and singularity formation in a coupled system of Yang-Mills-dilaton evolution equations

2003-06-11

arxiv.org/abs/hep-th/0306104v1

Phys.Rev. D68 (2003) 125010

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, 5 figures

Scientific paper

10.1103/PhysRevD.68.125010

We study both analytically and numerically a coupled system of spherically symmetric SU(2) Yang-Mills-dilaton equation in 3+1 Minkowski space-time. It has been found that the system admits a hidden scale invariance which becomes transparent if a special ansatz for the dilaton field is used. This choice corresponds to transition to a frame rotated in the $\ln r-t$ plane at a definite angle. We find an infinite countable family of self-similar solutions which can be parametrized by the $N$ - the number of zeros of the relevant Yang-Mills function. According to the performed linear perturbation analysis, the lowest solution with N=0 only occurred to be stable. The Cauchy problem has been solved numerically for a wide range of smooth finite energy initial data. It has been found that if the initial data exceed some threshold, the resulting solutions in a compact region shrinking to the origin, attain the lowest N=0 stable self-similar profile, which can pretend to be a global stable attractor in the Cauchy problem. The solutions live a finite time in a self-similar regime and then the unbounded growth of the second derivative of the YM function at the origin indicates a singularity formation, which is in agreement with the general expectations for the supercritical systems.

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