Polyakov backreaction in large D discretely self-similar collapse

Abstract

We study anomaly-induced semiclassical backreaction on an analytic family of discretely self-similar solutions of Einstein--Klein--Gordon theory at large spacetime dimension. Horizon regularity fixes a null-coordinate Floquet exponent and selects a unique regular quantum state. The Polyakov auxiliary field is affine-periodic rather than periodic, with a monodromy that is determined independently by a global zero-mode condition and by the conformal-coordinate scaling. Spherical reduction introduces a quantum coupling that grows toward the center, so the periodic first-order expansion is nonuniform. We construct the resulting nonlinear inner problem and find a critical dilaton surface. Generic crossings of this surface are singular, whereas matching to the regular zero-mass exterior selects a narrow, high-curvature throat. The anomaly also separates the effective null-energy boundaries from the classical matter flux and zero-curvature curves. These results show that the minimally coupled Polyakov model does not yield a generic smooth, exactly self-similar completion of the classical center.