AdS$$_{3}$$ spacetime wormhole fluctuations and their impact on false vacuum decay

Abstract In this work, we studied the boundary wormhole fluctuations of AdS $$_{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>3</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> spacetime and their impact on false vacuum decay. The model consists of three dimensional general relativity coupled to a real scalar field with self-interaction potential. Our analysis focuses on handlebody spacetimes, which correspond to boundary wormhole fluctuations. These fluctuations result in variations in the spacetime genus. Using the dilute wormhole gas approximation, we computed the boundary wormhole creation rate in the semiclassical region. Our results indicate that boundary wormholes are more likely to be created in spacetimes with larger absolute values of the cosmological constant. Furthermore, we find that smaller wormholes are more easily created compared to larger ones. Additionally, we investigated the impact of boundary wormhole fluctuations on false vacuum decay. The vacuum decay rate increases when the effects of wormhole fluctuations are considered. We show that all results remain qualitatively unchanged when certain parameter values are varied.