A search is performed for continuous gravitational waves emitted by unknown neutron stars in five nearby globular clusters using data from the third Laser Interferometer Gravitational-Wave Observatory (LIGO) observing run, over the frequency range –. The search uses a hidden Markov model to track both the frequency and phase of the continuous wave signal from one coherent segment to the next. It represents the first time that a phase-tracking hidden Markov model has been used in a LIGO search. After applying vetoes to reject candidates consistent with non-Gaussian artifacts, no significant candidates are detected. Estimates of the strain sensitivity at 95% confidence and corresponding neutron star ellipticity are presented. The best strain sensitivity, at , is achieved for the cluster NGC6544.

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