The Kähler Stability Wall in Perturbative Brane--Antibrane Inflation

Abstract

Perturbative brane--antibrane inflation requires the physical Kähler volume to remain stabilized while the anti-D3 sector supplies the inflationary energy. This paper shows that this requirement imposes an exact analytic boundary on the allowed anti-D3 tension. In the leading nilpotent effective theory, the Kähler minimum and the decompactification barrier disappear through a saddle-node degeneration determined by \(U_σ=U_{σσ}=0\). The positive-tension branch of this boundary is solved in closed form and uniformized by a single real parameter. The same solution fixes the local scaling of the Kähler mass, barrier height, and canonical distance to the endpoint. Integrating out the volume modulus reveals a Schur-complement singularity, showing that the adiabatic single-field description fails at the same boundary unless the inflaton--volume mixing is suppressed. The result is then translated into necessary flux-arithmetic filters involving the warped throat, D3 tadpole, conifold control, scalar normalization, and the full Kähler-sector mass matrix. Numerical tests verify the critical locus, the saddle-node scaling laws, and the resulting sparse throat-flux filtration. These conditions are necessary for compact realizations; no compact vacuum is asserted without the corresponding global and Wilsonian control checks.