One-Loop Effect of Null-Like Cosmology's Holographic Dual Super-Yang-Mills

TL;DR

This paper computes the one-loop effects in a super-Yang-Mills theory dual to a null-like cosmology with a big-bang singularity, revealing vanishing vacuum energy and potential non-renormalization properties.

Contribution

It demonstrates that certain time-dependent super-Yang-Mills theories have vanishing vacuum energy at one-loop and suggests a non-renormalization theorem for these models.

Findings

Vanishing 1-loop vacuum energy in the model.

Time-dependent cosmological constant contributions.

Suppression of higher derivative interactions under UV-finite conditions.

Abstract

We calculate the 1-loop effect in super-Yang-Mills which preserves 1/4-supersymmetries and is holographically dual to the null-like cosmology with a big-bang singularity. Though the bosonic and fermionic spectra do not agree precisely, we do obtain vanishing 1-loop vacuum energy for generic warped plane-wave type backgrounds with a big-bang singularity. Moreover, we find that the cosmological "constant" contributed either by bosons or fermions is time-dependent. The issues about the particle production of some background and about the UV structure are also commented. We argue that the effective higher derivative interactions are suppressed as long as the Fourier transform of the time-dependent coupling is UV-finite. Our result holds for scalar configurations that are BPS but with arbitrary time-dependence. This suggests the existence of non-renormalization theorem for such a new class of time-dependent theories. Altogether, it implies that such a super-Yang-Mills is scale-invariant, and that its dual bulk quantum gravity might behave regularly near the big bang.