We consider Deep Inelastic Scattering (DIS) thought experiments in unitary Conformal Field Theories (CFTs). We explore the implications of the standard dispersion relations for the OPE data. We derive positivity constraints on the OPE coefficients of minimal-twist operators of even spin s geq 2. In the case of s=2, when the leading-twist operator is the stress tensor, we reproduce the Hofman-Maldacena bounds. For s>2 the bounds are new.
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