Vacuum Ambiguity in de Sitter Space at Strong Coupling

It is well known that in the weak coupling regime, quantum field theories in de Sitter space do not have a unique vacuum, but a class of vacua parametrized by a complex parameter $\alpha$, i.e., the so-called $\alpha$-vacua. In this article, using gauge/gravity duality, we calculate the symmetric two-point function of strongly coupled $\mathcal{N}=4$ supersymmetric Yang-Mills theory on $d{S}_3$. We find that there is a class of de Sitter invariant vacua, parametrized by a set of complex parameters $\{{\alpha }_{\nu }\}$.