We predict a field-free transverse Josephson diode effect in altermagnets (AMs) with Rashba spin-orbit coupling, achieving diode efficiencies exceeding $3000\%$ and unidirectional transverse supercurrents in four-terminal junctions. In this geometry, a longitudinal phase bias generates transverse supercurrents that exhibit nonreciprocity and a finite anomalous phase shift, while the longitudinal current itself displays a Josephson diode effect. Both responses are tunable via the Néel vector orientation. We further show that the effect remains robust against moderate disorder, imperfect interfaces and persists up to the superconducting transition temperature. These results establish AMs as a promising platform for nonreciprocal superconducting transport, with clear routes toward experimental realization.

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• Josephson effect
• Altermagnets
• Josephson junctions
• Bogoliubov-de Gennes equations