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arXiv · 0807.1517

Gauge Theories with Time Dependent Couplings and their Cosmological Duals

Adel Awad·Sumit R. Das·Suresh Nampuri·K. Narayan·Sandip P. Trivedi
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Abstract

We consider the N=4 SYM theory in flat 3+1 dimensional spacetime with a time dependent coupling constant which vanishes at $t=0$, like $g_{YM}^2=t^p$. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at $t=0$, for a generic state. In addition, if $p>1$ the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past $t=0$. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyond $t=0$. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a space-like singularity at $t=0$. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains non-zero and becomes small at $t=0$, the curvature in the bulk becomes of order the string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.

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Adel Awad, Sumit R. Das, Suresh Nampuri, K. Narayan, Sandip P. Trivedi. 2009-05-21. Gauge Theories with Time Dependent Couplings and their Cosmological Duals. https://doi.org/10.1103/physrevd.79.046004

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