Estimating global charge violating amplitudes from wormholes

TL;DR

This work investigates how global charge violation manifests in quantum gravity by analyzing high-energy scattering of spherically symmetric shells in AdS spacetimes. It identifies a wormhole topology that estimates the squared amplitude $|\mathcal{A}|^2$ for charge-violating transitions and relates the result to black-hole entropy, yielding an exponential suppression $|\mathcal{A}|^2 \sim e^{-S(E)}$ in suitable regimes. The authors develop a robust bulk construction, including a bow-tie geometry with large Lorentzian evolution, and provide a boundary interpretation in terms of factorized correlators and thermofield-double-like states, highlighting the role of averaging over microscopic data. They also discuss the implications for gauged versus global symmetries, potential flat-space limits, and connections to JT gravity, offering a framework to bound symmetry-violating effects from quantum gravity.

Abstract

We consider the scattering of high energy and ultra relativistic spherically symmetric shells in asymptotically AdS$_D$ spacetimes. We analyze an exclusive amplitude where a single spherically symmetric shell goes in and a single one comes out, such that the two have different global symmetry charges of the effective gravity theory. We study a simple wormhole configuration that computes the square of the amplitude and analyze its properties.

Figures (11)

• Figure 1: Sketch of the topology of the wormhole we will consider. The two sides are setting up the computation of ${\cal A}$ and ${\cal A}^*$ respectively.
• Figure 2: Single shell solution. We suppressed the $S^{d-1}$, only the Euclidean time and radial directions are indicated here. The dot at the center indicates a fixed point of the $U(1)$ isometry.
• Figure 3: (a) Euclidean picture. The shell can be viewed as computing a two point function. We can view the cut along the dotted line as the state created by the operator. (b) Picture we obtain after we evolve the state from (a) into Lorentzian time. The dashed line is the horizon.
• Figure 4: Two shell solution when $E< E'$. The central region, with energy $E$, contains fixed point of the isometry, but the other two regions do not contain fixed points. The operators $A$ and $B$ are separated by a positive Euclidean evolution $\tau_{AB}>0$.
• Figure 5: Two shell solution for $E> E'$. The central region involves negative euclidean time evolution. Lines of the same color are identified. This means that the euclidean time separation $\tau_{AB}$ between $A$ and $B$ along the boundary of the yellow region is negative.