Kosmic Field Theories: Towards Holographic Duals for Unitary String Cosmologies

TL;DR

This paper proposes a new class of large-N holographic gauge theories called Kosmic Field Theories (KFTs) that match unitarity conditions of cosmological amplitudes and explore their properties across different dimensions.

Contribution

Introduction of Kosmic Field Theories (KFTs) with complex phases that satisfy bulk unitarity conditions and their analysis across various dimensions, including implications for cosmology.

Findings

KFTs' n-point functions match unitarity conditions in bulk.

No overlap between KFTs and Wick rotations of unitary QFTs.

Features are more favorable in odd dimensions, allowing real N^2 and potential string duals.

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.