A holographic dual of CFT with flavor on de Sitter space

We introduce a D7-brane probe in AdS(5) x S-5 background in a way that the 4d part of the induced metric on D7-brane becomes 4d de-Sitter space (dS(4)) inside AdS(5) instead of 4d Minkowski space. Although supersymmetry is completely broken, we obtain a static configuration and show the absence of dynamical tachyonic modes. Following holographic renormalization we renormalize the Dirac-Born-Infeld action of D7-brane and we completely fix the counter terms including finite contributions from the consistency under various limits. Through the AdS/CFT correspondence we study the chiral condensate and meson spectrum of CFT dual theory on dS4 where the energy scale is identified with the direction normal to dS4 space in AdS5. We identify and properly reproduce the finite temperature effects on dS4. Our results support the holographic interpretation of the Randall-Sundrum model with non fine-tuned dS4 brane(s) and the holography between AdSp (or dSp) bulk gravity and CFT on dSp-1 called the (A) dS/dS correspondence.