Cosmic string cusps produce powerful bursts of gravitational waves (GWs).
These bursts provide the most promising observational signature of cosmic
strings. In this letter we report stringent limits on cosmic string models
obtained from the analysis of 625 days of observation with the LIGO and Virgo
GW detectors. A significant fraction of the cosmic string parameter space is
ruled out. This result complements and improves existing limits from searches
for a stochastic background of GWs using cosmic microwave background and pulsar
timing data. In particular, if the size of loops is given by gravitational
back-reaction, we place upper limits on the string tension $Gmu$ below
$10^{-8}$ in some regions of the cosmic string parameter space.
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