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Aspects of the map from Exact RG to Holographic RG in AdS and dS
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Aspects of the map from Exact RG to Holographic RG in AdS and dS
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In earlier work the evolution operator for the exact RG equation was mapped to a field theory in Euclidean AdS. This gives a simple way of understanding AdS/CFT. We explore aspects of this map by studying a simple example of a Schroedinger equation for a free particle with time dependent mass. This is an analytic continuation of an ERG like equation. We show for instance that it can be mapped to a harmonic oscillator. We show that the same techniques can lead to an understanding of dS/CFT too.
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$SO(1, d + 1)$ symmetry of the Exact RG equation
The ERG evolution operator is SO(1,d+1)-invariant for any admissible cutoff, with cutoff-dependent conformal generators that reduce to standard AdS isometries for the special AdS-mapping cutoff.
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