Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-07-09
Phys.Rev.D79:046004,2009
Physics
High Energy Physics
High Energy Physics - Theory
45 pages, 1 figure; v2. minor modifications; v3: PRD version, conclusions in the field theory case significantly revised to in
Scientific paper
10.1103/PhysRevD.79.046004
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.
Awad Ahmad A.
Das Sumit R.
Nampuri Suresh
Narayan K.
Trivedi Sandip P.
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