2008/07/31 by Adel Awad, Sumit R. Das, Suresh Nampuri +2 · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevd.79.046004
published as Phys.Rev.D79:046004,2009 · 45 pages, 1 figure; v2. minor modifications; v3: PRD version, conclusions in the field theory case significantly revised to include possible renormalization effects, quantum mechanics toy model unchanged, abstract and introduction revised, additional subsection 4.1 added
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 gYM2=tp. 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.