One-loop effect of null-like cosmology's holographic dual super-Yang–Mills

We calculate the 1-loop effect in super-Yang-Mills which preserves1/4-supersymmetries and is holographically dual to the null-like cosmology witha big-bang singularity. Though the bosonic and fermionic spectra do not agreeprecisely, we do obtain vanishing 1-loop vacuum energy for generic warpedplane-wave type backgrounds with a big-bang singularity. Moreover, we find thatthe cosmological "constant" contributed either by bosons or fermions istime-dependent. The issues about the particle production of some background andabout the UV structure are also commented. We argue that the effective higherderivative interactions are suppressed as long as the Fourier transform of thetime-dependent coupling is UV-finite. Our result holds for scalarconfigurations that are BPS but with arbitrary time-dependence. This suggeststhe existence of non-renormalization theorem for such a new class oftime-dependent theories. Altogether, it implies that such a super-Yang-Mills isscale-invariant, and that its dual bulk quantum gravity might behave regularlynear the big bang.Comment: 20 pages, v2 add comments and references, v3 clarify BPS condition & add new discussion on particle production and UV structure, v4&v5 minor changes, final to JHE