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Phys."],"published-print":{"date-parts":[[2019,11]]},"abstract":"<jats:title>A<jats:sc>bstract<\/jats:sc>\n                     <\/jats:title><jats:p>We explore the space of consistent three-particle couplings in \u2124<jats:sub>2<\/jats:sub>-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the two-to-two scattering amplitudes and extends the techniques of [2] to a multi-amplitude setup. Our second approach is based on placing QFTs in AdS to get upper bounds on couplings with the numerical conformal bootstrap, and is a multi-correlator version of [1]. The space of allowed couplings that we carve out is rich in features, some of which we can link to amplitudes in integrable theories with a \u2124<jats:sub>2<\/jats:sub> symmetry, e.g., the three-state Potts and tricritical Ising field theories. 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