We demonstrate a new technique for detecting radio transients based on interferometric closure quantities. The technique uses the bispectrum, the product of visibilities around a closed-loop of baselines of an interferometer. The bispectrum is calibration independent, resistant to interference, and computationally efficient, so it can be built into correlators for real-time transient detection. Our technique could find celestial transients anywhere in the field of view and localize them to arcsecond precision. At the Karl G. Jansky Very Large Array (VLA), such a system would have a high survey speed and a 5-sigma sensitivity of 38 mJy on 10 ms timescales with 1 GHz of bandwidth. The ability to localize dispersed millisecond pulses to arcsecond precision in large volumes of interferometer data has several unique science applications. Localizing individual pulses from Galactic pulsars will help find X-ray counterparts that define their physical properties, while finding host galaxies of extragalactic transients will measure the electron density of the intergalactic medium with a single dispersed pulse. Exoplanets and active stars have distinct millisecond variability that can be used to identify them and probe their magnetospheres. We use millisecond time scale visibilities from the Allen Telescope Array (ATA) and VLA to show that the bispectrum can detect dispersed pulses and reject local interference. The computational and data efficiency of the bispectrum will help find transients on a range of time scales with next-generation radio interferometers.
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