= Validity of the abelian BIon approximation
The <DBI action> resums field strengths but truncates their <derivative expansion>. A slowly varying large-charge throat may therefore be controlled even when its field strengths are not small. Large derivatives, large embedding curvature, string loops and gravitational backreaction restrict this description, and its ideal singular core is not uniformly controlled. The electric throat window $|N|g_s\gg1$, $g_s^2|N|\ll1$ and magnetic window $|N|\gg1$, $g_s|N|\ll1$ separate derivative and backreaction requirements.
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