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We study anti-holomorphic involutions of the moduli space of principal$G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a complexsemisimple Lie group. These involutions are defined by fixing anti-holomorphicinvolutions on both $X$ and $G$. We analyze the fixed point locus in the modulispace and their relation with representations of the orbifold fundamental groupof $X$ equipped with the anti-holomorphic involution. We also study therelation with branes. This generalizes work byBiswas--Garc\'{\i}a-Prada--Hurtubise and Baraglia--Schaposnik.

Anti-holomorphic involutions of the moduli spaces of Higgs bundles