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Celestial holography is a new way to understand flat-space amplitudes.Self-dual theories, due to their nice properties, are good subjects to studycelestial holography. In this paper, we developed a new formula to calculatethe celestial color-ordered self-dual Yang-Mills amplitudes based on celestialBerends-Giele currents, which makes the leading OPE limit manifest. Inaddition, we explore some higher-order terms of OPE in the celestial self-dualYang-Mills theory.

Celestial self-dual Yang-Mills theory: a new formula and the OPE limit