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$χ\rm{SB}$ of cascading gauge theory in de Sitter

${\cal N}=1$ supersymmetric $SU(N)\times SU(N+M)$ cascading gauge theory of Klebanov et.al spontaneously breaks chiral symmetry in Minkowski space-time. We demonstrate that in de Sitter space-time the chiral symmetry breaking occurs for the values of the Hubble constant $H\lesssim 0.7 Λ$, as well as in a narrow window $0.92(1) Λ\le H\le 0.92(5) Λ$. We give a precise definition of the strong coupling scale $Λ$ of cascading gauge theory, which is related to the glueball mass scale in the theory $m_{glueball}$ and the asymptotic string coupling $g_s$ as $Λ\sim g_s^{1/2} m_{glueball}$.