Modified Einstein equations from the 1-loop effective action of the IKKT model

We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with extra contributions from dilaton and axionic fields, as well as a novel anharmonicity tensor Cµν capturing the classical Yang–Mills-type action. The resulting gravity theory approximately reduces to general relativity in some regime, but differs significantly at cosmic scales, leading to an asymptotically flat Friedmann–Lemaître–Robertson–Walker cosmological evolution governed by the classical action.