Quantum Probe to the Higher Dimensional Yang-Mills Singularity

We investigate the quantum nature of naked curvature singularities in Einstein-Yang-Mills (EYM) theory using the Horowitz-Marolf (HM) criterion, which assesses quantum singularities via the evolution of quantum scalar fields. Focusing on timelike singularities in spacetime dimension $D \geq 5$, we analyze both pure Yang-Mills and Einstein-Maxwell-Yang-Mills (EMYM) solutions. We then incorporate higher curvature corrections through Gauss-Bonnet (GB) terms. From positivity requirement the expression under square root that arises in GB may create a secondary singularity that shall be scrutinized carefully. Our analysis reveals that while EYM and EMYM spacetimes remain quantum mechanically singular, the inclusion of GB corrections can, in general, render the singularity quantum mechanically regular for specific values of the mass parameter $m$, which is related to the YM charge $Q$ in $D = 5$ space-time dimensions. Contrary, for space-time dimension $D \geq 6$, although the outer (secondary) singularity may be healed quantum mechanically for certain values of the mass parameter $m$, the central singularity remains quantum mechanically singular.