Kosmic Field Theories: towards holographic duals for unitary string cosmologies

A

bstract

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 λ , 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 /λ 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 ± sign of N ² and λ .

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.