Moduli stabilization and the holographic RG for AdS and dS

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 dS D−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 AdS D and dS D . 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.

Holographic RG flows, entanglement entropy and the sum rule

“…The reason is that various aspects of the holographic RG simplify in the Hamiltonian approach, as found in [42][43][44], and more recently in [45][46][47]. 5…”

De Sitter holography and entanglement entropy

“…This would generically not produce the same sharp agreement, but there may be special flows that also fit the facts. In [28], we found that if one treats one side, e.g. w < w uv in dS d+1 , as the gravity dual of a matter theory, this theory has a highly constrained holographic Wilsonian RG flow: single-trace operators do not flow, and higher traces are determined in terms of lower ones.…”

“…One aspect of this is that the dual matter sectors only behave as a pair of CFTs at sufficiently low energies; they are deformed by irrelevant operators. 4 3 dS d+1 is a very special Randall-Sundrum [27] system, with no explicit Planck brane and a highly constrained holographic RG flow [28]. The d-dimensional gravity is dynamical at finite times, and we will be concerned with the period over which the spacetime is classically de Sitter.…”

“…Having identified the part of the CFT Hilbert space that comes into the holographic description of a long-lived de Sitter geometry, we should stress that the full system has more degrees of freedom which enter in the later decay of de Sitter [23,28], in contrast to proposals with a finite total number of degrees of freedom such as [43,44]. In both cases, however, the finite number of states relevant for the dual description of a long-lived de Sitter configuration is related to backreaction on its geometry.…”

“…There is a suite of calculations checking the basic structure of the duality [18,[21][22][23]28]. Of course, the tools are more limited in this cosmological context.…”