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The astrophysical origin of gravitational wave (GW) events discovered byLIGO/VIRGO remains an outstanding puzzle. In active galactic nuclei (AGN),compact-object binaries form, evolve, and interact with a dense star clusterand a gas disk. An important question is whether and how binaries merge inthese environments. To address this question, we have performed one-dimensional$N$-body simulations combined with a semi-analytical model which includes theformation, disruption, and evolution of binaries self-consistently. We pointout that binaries can form in single-single interactions by the dissipation ofkinetic energy in a gaseous medium. This ``gas capture'' binary formationchannel contributes up to $97\,\%$ of gas-driven mergers and leads to a highmerger rate in AGN disks even without pre-existing binaries. We find the mergerrate to be in the range $\sim 0.02-60\,\mathrm{Gpc^{-3}yr^{-1}}$. The resultsare insensitive to the assumptions on gaseous hardening processes: we find thatonce they are formed, binaries merge efficiently via binary-single interactionseven if these gaseous processes are neglected. We find that the average numberof mergers per BH is $0.4$, and the probability for repeated mergers in 30 Myris $\sim 0.21-0.45$. High BH masses due to repeated mergers, higheccentricities, and a significant Doppler drift of GWs are promising signatureswhich distinguish this merger channel from others. Furthermore, we find thatgas-capture binaries reproduce the distribution of LMXBs in the Galacticcenter, including an outer cutoff at $\sim1$ pc due to the competition betweenmigration and hardening by gas torques.

Formation and Evolution of Compact Object Binaries in AGN Disks