Kosmic Field Theories: Towards Holographic Duals for Unitary String Cosmologies

Abstract

Recent work on cosmological amplitudes has established reality conditions (derived from unitarity) for general particle-creation processes in flat FLRW cosmologies, in the Bunch-Davies wavefunction. In light of these results, we propose a new class of large-$N$ holographic gauge theories with $d$ spatial dimensions, which we call Kosmic Field Theories (KFTs), of which only a subset are conformal (KCFTs). By imposing an appropriate -- $d$ dependent -- complex phase for the number of colours $N$ and the t' Hooft coupling $\lambda$, we show that the complex phases of $n$-point functions in a KFT match the reality conditions required by $d + 1$ bulk unitarity, to all orders in bulk and boundary perturbation theory, including loop diagrams. Since $N^2/\lambda$ is imaginary in all dimensions, the class of (parity-even) KFTs has no overlap with the class of Wick rotations of unitary QFTs. We also make a preliminary investigation of positivity conditions, which might constrain the overall $\pm$ sign of $N^2$ and $\lambda$. Although SU($N$) models with adjoint matter can be defined in generic real dimensions $d$, several features of the class of KFTs are nicer when $d$ is odd, allowing $N^2$ to be real. This includes the possibility of non-oriented and/or open string duals, reality of the effective number of degrees of freedom, and closure under RG flow beyond the leading order in a $1/N$ expansion. This could explain why we live in a cosmology with an even number of spacetime dimensions.