We propose and study a holographic dual of the type-IIB superstring theory of ${\mathrm{AdS}}_5\times S^5$ in terms of the $\mathcal{N}=4$ superconformal Yang-Mills theory on ${\mathrm{dS}}_4$. We develop the bulk to boundary formalism for the computation of the correlation functions to a wide class of theories. We apply it to compute the two-point correlators in the particular duality under study and we find that they agree with the expected results in $dS$ conformal field theory. The gauge theory is expected to be UV finite and enjoy exact $SL(2,Z)$ strong-weak duality. As the string theory Green-Schwarz sigma model carries an infinite number of classically conserved charges, it also suggests that the superconformal Yang-Mills theory is integrable and deserves further studies.

• Received 16 June 2016

DOI:https://doi.org/10.1103/PhysRevD.94.106013