Brauer group of moduli of stable parabolic SL(r,C) and PGL(r, C) -connections and Higgs bundles over a curve

Let X be a compact Riemann surface of genus at least 3. We compute the Brauer groups of the moduli spaces of stable parabolic \text{SL}(r,\mathbb{C})-connections and stable strongly parabolic \text{SL}(r,\mathbb{C})-Higgs bundles over X. We also establish an equality of the Brauer group of the moduli stack of stable parabolic \text{PGL}(r,\mathbb{C})-connections and the smooth locus of its coarse moduli space.