"Filtering" CFTs at large N: Euclidean Wormholes, Closed Universes, and Black Hole Interiors

TL;DR

This paper introduces a large-N filter in holography that clarifies the role of Euclidean wormholes, resolves the factorization puzzle, and explains the emergence of complex spacetime structures like black hole interiors and baby universes.

Contribution

It proposes a boundary-based large-N filter that projects out erratic N-dependence, resolving key puzzles in holography and enabling the emergence of richer spacetime geometries.

Findings

Provides a boundary definition of gravitational averages.

Derives inequalities constraining wormhole amplitudes.

Suggests black hole interiors and baby universes are quantum volatile.

Abstract

Despite its successes, the large-$N$ holographic dictionary remains incomplete. Key features of gravitational path integrals--most notably Euclidean wormholes and the associated failure of factorization--lack a clear interpretation in the standard large-$N$ framework. A related challenge is the possibility of erratic $N$-dependence in CFT observables, behavior with no evident semiclassical gravitational counterpart. We argue that these puzzles point to a missing ingredient in the dictionary: a large-$N$ filter. This filter projects out the erratic $N$-dependence of CFT quantities when mapping them to semiclassical bulk physics, providing an intrinsic boundary definition of gravitational "averages." It also offers a boundary explanation of wormhole contributions and a boundary prediction of their amplitudes, thereby giving a natural resolution of the factorization puzzle. In addition, we derive an infinite tower of inequalities constraining wormhole amplitudes and argue that internal wormholes do not induce random couplings in the low-energy effective theory. Beyond resolving factorization, the large-$N$ filter supplies a generalized framework from which richer Lorentzian spacetime structures can emerge, including closed universes and black hole interiors. We argue that, as a consequence of erratic large-$N$ behavior, both closed universes and black hole interiors are quantum volatile, and that an AdS spacetime entangled with a baby universe is likewise quantum volatile. This volatility may allow an observer in AdS to infer the existence of the baby universe, whereas for an infalling observer, the ability to make measurements near a black hole horizon may become fundamentally limited--even if they may not live long enough to notice.