Baby Universes, Holography, and the Swampland
On the basis of a number of Swampland conditions, we argue that the Hilbert space of baby universe states must be one-dimensional in a consistent theory of quantum gravity. This scenario may be interpreted as a type of “Gauss’s law for entropy” in quantum gravity, and provides a clean synthesis of the tension between Euclidean wormholes and a standard interpretation of the holographic dictionary, with no need for an ensemble. Our perspective relies crucially on the recently-proposed potential for quantum-mechanical gauge redundancies between states of the universe with different topologies. We further comment on the possible exceptions in d ≤ 3 for this hypothesis and the role of an ensemble in holographic theories in the context of theories of quantum gravity in d = 2 (such as JT gravity and possible cousins in d = 3), which we argue are incomplete physical theories that should be viewed as branes in a higher dimensional theory of quantum gravity for which an ensemble plays no role.
Authors:
;
Award ID(s):
Publication Date:
NSF-PAR ID:
10181586
Journal Name:
ArXivorg
Page Range or eLocation-ID:
1 - 25
ISSN:
2331-8422
3. A bstract The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ‖ ϕ ‖ as m ~ exp(− λ ‖ ϕ ‖), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $$1/\sqrt{d-2}$$ 1 / d − 2 . In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $$1/\sqrt{d-2}$$ 1 / d − 2 discussed previously in the literature are always accompanied by even lighter towersmore »