Abstract
Abstract We relate moduli stabilization (V ′ = 0) in the bulk of AdS D or dS D to basic properties of the Wilsonian effective action in the holographic dual theory on dSD−1: the single-trace terms in the action have vanishing beta functions, and higher-trace couplings are determined purely from lower-trace ones. In the de Sitter case, this encodes the maximal symmetry of the bulk spacetime in a quantity which is accessible within an observer patch. Along the way, we clarify the role of counterterms, constraints, and operator redundancy in the Wilsonian holographic RG prescription, reproducing the expected behavior of the trace of the stress-energy tensor in the dual for both AdSD and dSD . We further show that metastability of the gravity-side potential energy corresponds to a nonperturbatively small imaginary contribution to the Wilsonian action of pure de Sitter, a result consistent with the need for additional degrees of freedom in the holographic description of its ultimate decay.
Highlights
One would like to understand what specifications are required of the matter sector1 in the dual in order for it to reconstruct the physics of an observer patch of dS.2
We further show that metastability of the gravity-side potential energy corresponds to a nonperturbatively small imaginary contribution to the Wilsonian action of pure de Sitter, a result consistent with the need for additional degrees of freedom in the holographic description of its ultimate decay
We find that the single-trace couplings in the holographic dual do not run, and that the higher-trace couplings are determined purely from lower-trace ones in the Wilsonian action
Summary
Let us start by explaining our basic framework and results. Much of this is in direct parallel with the analysis in [10], generalized appropriately to the case of a dSD−1 foliation of the bulk. We will need to clarify the role of the warp factor and include appropriate counterterms to obtain standard AdS/CFT operator redundancies, applying [12, 21] to the Wilsonian Holographic RG. Our main result is that the scale-invariance of the singletrace couplings is a consequence of moduli stabilization for dS as well as AdS, and that in both cases the higher-trace couplings are determined in terms of the lower-trace ones
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