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 dS_4 where the energy scale is identified with the direction normal to dS_4 space in AdS_5. We identify and properly reproduce the finite temperature effects on dS_4. Our results support the holographic interpretation of the Randall-Sundrum model with non fine-tuned dS_4 brane(s) and the holography between AdS_p (or dS_p) bulk gravity and CFT on dS_{p-1} called the (A)dS/dS correspondence.