Constraints on self-dual black hole in loop quantum gravity with S0-2 star in the galactic center

One of remarkable features loop quantum gravity (LQG) is that it can provide resolutions to both the black hole and big bang singularities. In mini-superspace approach based on polymerization procedure in LQG, a corrected metric constructed. This also known as self-dual spacetime since form invariant under exchange $r \to a_0/r$ with $a_0$ being proportional minimum area LQG $r$ standard radial coordinate at asymptotic infinity. It modifies Schwarzschild by polymeric function $P$, purely due geometric effects from LQG. Here $P$ related parameter $\delta$ which introduced define paths one integrates connection along holonomies Hamiltonian constraint this paper, we consider its orbital signatures S0-2 star orbiting Sgr A* central region our Milky Way, compare publicly available astrometric spectroscopic data, including positions, velocities, precession for star. We perform Monte Carlo Markov Chain (MCMC) simulations probe possible orbit No significant evidence arisIng found. thus place an upper bounds 95\% confidence level $P < 0.043$ 0.056$, Gaussian uniform priors parameters, respectively.