Quantum Gates to other Universes

TL;DR

This work builds a holographic model in which two AdS4 universes are joined by a microscopic gate, a low-rank gauge group acting as a messenger, with the dual gravity description featuring a short AdS5×S5 throat carrying $n$ flux units. The authors derive a universal graviton-mass mixing relation $M^2 \simeq {3 n^2 (\kappa_4^2 + \kappa_4'^{2}) \over 16\pi^2}$, which reduces to $M^2 \simeq {3 \over 8\pi^2} \kappa_4^2 n^2$ for identical universes, and show that the effective coupling is quantized—paralleling double-trace deformations but preserving locality once the gate is integrated back. The holographic construction uses partitions of good 3d ${\cal N}=4$ quivers, realized as Type-IIB solutions with harmonic functions $h_1,h_2$, and the gate is implemented by a rearrangement of $n$ boxes in the quiver diagrams, corresponding to a calculable AdS5 throat geometry. The results bridge field-theoretic double-trace intuition and a local, semiclassical gravitational mechanism for inter-Universe coupling, with extensions to non-identical universes and potential worldsheet interpretations of gates.

Abstract

We present a microscopic model of a bridge connecting two large Anti-de-Sitter Universes. The Universes admit a holographic description as three-dimensional ${\cal N}=4$ supersymmetric gauge theories based on large linear quivers, and the bridge is a small rank-$n$ gauge group that acts as a messenger. On the gravity side, the bridge is a piece of a highly-curved AdS$_5\times$S$_5$ throat carrying $n$ units of five-form flux. We derive a universal expression for the mixing of the two massless gravitons: $M^2 \simeq 3n^2 (κ_4^2 + κ_4^{\prime\,2})/16π^2$, where $M$ is the mass splitting of the gravitons, $κ_4^2, κ_4^{\prime\,2}$ are the effective gravitational couplings of the AdS$_4$ Universes, and $n$ is the quantized charge of the gate. This agrees with earlier results based on double-trace deformations, with the important difference that the effective coupling is here quantized. We argue that the apparent non-localities of holographic double-trace models are resolved by integrating-in the (scarce) degrees of freedom of the gate.

Figures (8)

• Figure 1: Two large quivers corresponding to two large AdS Universes joined by a gate which is a low-rank gauge theory coupling via bifundamental matter to the quivers.
• Figure 2: The Young diagram $\rho$ and its transpose $\rho^T$ inscribed in their respective grids.
• Figure 3: The magnetic quiver for the ordered pair of partitions $(\rho, \hat{\rho})$. The gauge-group ranks $n_j$ and the flavor-group ranks $m_j$ can be expressed in terms of the row lengths of $\rho$ and $\hat{\rho}^T$. The inequality $\hat{\rho}^T > \rho$ guarantees the positivity of all $n_j$.
• Figure 4: The operation $C$ that replaces $\rho$ by its complement inside the $N\times \hat{N}$ grid, and $\hat{\rho}$ by its complement inside the $N\times \hat{N}$ grid. $C$ changes black to white and rotates the diagram by 180$^o$.
• Figure 5: The Young diagrams $(\rho, \hat{\rho})$ corresponding to two decoupled theories $(\rho_1, \hat{\rho}_1)$ and $(\rho_2, \hat{\rho}_2)$.