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We present dyon solutions to an SU(2) Dirac-Born-Infeld (DBI) gauge theorycoupled to a Higgs triplet. We consider different non-Abelian extensions of theDBI action and study the resulting solutions numerically, comparing them withthe standard Julia-Zee dyons. We discuss the existence of a critical value of$\beta$, the Born-Infeld absolute field parameter, below which the solutionceases to exist. We also analyse the effect of modifying the DBI action so asto include the analogous of the $\theta$ term, showing that Witten formula forthe dyon charge also holds in DBI theories.Comment: 15 pages, 3 figure

Monopoles, dyons, and the theta term in Dirac-Born-Infeld theory