The dual of nothing

TL;DR

The paper investigates time-dependent bulk spacetimes in the AdS/CFT framework by constructing bubbles of nothing through double analytic continuation of AdS black holes (Schwarzschild, Kerr, RN) in $AdS_5\times S^5$. The resulting spacetimes are asymptotically locally AdS with a conformal boundary $dS_3 \times S^1$, and are conjectured to be dual to ${\cal N}=4$ SYM on that time-dependent background; holographic renormalization yields a boundary stress tensor whose universal anomaly part matches the field theory conformal anomaly, while a state-dependent piece encodes the bubble parameters. The analysis reveals multiple bubble branches with distinct stability properties, and explores how rotation and charge introduce new parameters without eliminating the asymptotic identifications. Overall, the work demonstrates how bulk time dependence is reflected in the dual field theory and points to future directions in connecting bulk particle production to boundary dynamics and in finding more tractable time-dependent AdS solutions.

Abstract

We consider ``bubbles of nothing'' constructed by analytically continuing black hole solutions in Anti-de Sitter space. These provide interesting examples of smooth time-dependent backgrounds which can be studied through the AdS/CFT correspondence. Our examples include bubbles constructed from Schwarzschild-AdS, Kerr-AdS and Reissner-Nordstrom AdS. The Schwarzschild bubble is dual to Yang-Mills theory on three dimensional de Sitter space times a circle. We construct the boundary stress tensor of the bubble spacetime and relate it to the properties of field theory on de Sitter.

Figures (1)

• Figure 1: Periodic identification of $\chi$ in global coordinates in the $t=0$ slice. The figure shows the radial coordinate in AdS and $\psi$. Over every point in the figure there is a 2-sphere. The locus of points of fixed $\chi$ is shown.