We study production of gravitational waves (GWs) in strongly supercooled cosmological phase transitions in gauge theories. We extract from two-bubble lattice simulations the scaling of the GW source, and use it in many-bubble simulations in the thin-wall limit to estimate the resulting GW spectrum. We find that in presence of the gauge field the GW source decays with bubble radius as $propto R^{-3}$ after collisions. This leads to a GW spectrum that follows $Omega_{rm GW} propto omega^{2.3}$ at low frequencies and $Omega_{rm GW} propto omega^{-2.9}$ at high frequencies, marking a significant deviation from the popular envelope approximation.
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