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

Avik Chakraborty, Jewel Kumar Ghosh, Martín Molina, Ayan Mukhopadhyay

TL;DR

This work shows that in Lorentzian $\mathrm{dS}_3$, gravitational junctions between two copies of de Sitter space reproduce the non-linear Nambu-Goto dynamics for a closed string, with transient vibrations about the equator sourced by gravitational memory from $\mathcal{I}^-$ and dissolving into memory at $\mathcal{I}^+$. Through perturbative analysis in the dimensionless tension $\lambda=8\pi G_N T_0 L$, the authors decompose linear string fluctuations into transient and persistent modes, and demonstrate memory encoded as relative time and angular reparametrizations across the junction, which in turn define self-consistent clocks. They also construct a non-perturbative exact solution, showing how large tension can qualitatively alter the spacetime structure (doubling or destroying $dS_3$ at $\tau=0$). Collectively, the results suggest extended objects like strings are central to defining quantum gravity in de Sitter space and may illuminate dS/CFT interfaces via memory-induced maps between early and late boundaries.

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 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 solutions of the junction conditions also reveal that a transient string excitation sets up a clock self-consistently without the need of an external observer.

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

TL;DR

This work shows that in Lorentzian , gravitational junctions between two copies of de Sitter space reproduce the non-linear Nambu-Goto dynamics for a closed string, with transient vibrations about the equator sourced by gravitational memory from and dissolving into memory at . Through perturbative analysis in the dimensionless tension , the authors decompose linear string fluctuations into transient and persistent modes, and demonstrate memory encoded as relative time and angular reparametrizations across the junction, which in turn define self-consistent clocks. They also construct a non-perturbative exact solution, showing how large tension can qualitatively alter the spacetime structure (doubling or destroying at ). Collectively, the results suggest extended objects like strings are central to defining quantum gravity in de Sitter space and may illuminate dS/CFT interfaces via memory-induced maps between early and late boundaries.

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 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 solutions of the junction conditions also reveal that a transient string excitation sets up a clock self-consistently without the need of an external observer.
Paper Structure (2 sections, 30 equations, 1 figure)

This paper contains 2 sections, 30 equations, 1 figure.

Table of Contents

  1. Nambu-Goto at non-linear order
  2. A non-perturbative solution

Figures (1)

  • Figure 1: A two-way junction formed by gluing dS$_3$ manifolds $\mathcal{M}_1$ and $\mathcal{M}_2$. The points $P_1$ and $P_2$ on $\Sigma_1$ on $\Sigma_2$, respectively are identified. The shaded portions of $\mathcal{M}_1$ and $\mathcal{M}_2$ are discarded before gluing.