Junctions, strings, clocks and gravitational memory in three dimensional dS space

Abstract

We show that non-trivial stringy excitations in Lorentzian three dimensional de Sitter spacetime can be created self-consistently from gravitational memory in the infinite past. In addition to demonstrating that the Nambu-Goto equations for the string emerge from the two-way gravitational junction conditions, we establish the existence of well-behaved solutions corresponding to transient fluctuations of a closed string about the equator which are both borne out of and dissolve to distinct gravitational memory in the infinite past and future, respectively. The memory at infinite past, which uniquely characterizes such a solution, is a single function giving the relative angular shift at the junction gluing two two-dimensional hemispheres. This reveals that a clock dynamically emerges in the presence of a gravitational junction without the need of any external observer. We also show that our results generalize to the $n$-way gravitational junctions with $n\geq 3$, which are captured by Nambu-Goto-Monge-Ampère equations for coupled $n-1$ strings -- these degrees of freedom exist even in the tensionless limit. Furthermore, for $n\geq 3$, $n-1$ correlated clocks dynamically emerge without the need of external observers in the tensionless limit, revealing a novel feature of pure three-dimensional gravity.