The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
The giant graviton expansion
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Finite-N BMN index summed over all vacuum sectors for N≤9 reveals order-N² entropy growth that survives the sum and dominance switching from single- to double-partition sectors starting at N=5.
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.
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Fermionic trace relations and supersymmetric indices at finite $N$
The supersymmetric index in a one-fermion matrix model for N=4 SYM is independent of N due to exact cancellations between bosonic and fermionic trace relations.
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Finite-$N$ BMN index across all vacuum sectors
Finite-N BMN index summed over all vacuum sectors for N≤9 reveals order-N² entropy growth that survives the sum and dominance switching from single- to double-partition sectors starting at N=5.
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Inner Horizon Saddles and a Spectral KSW Criterion
Inner horizon saddles supply the semiclassical correction -exp(A_inner/4G) to near-extremal black-hole entropy and motivate a spectral KSW criterion for well-defined one-loop effects around complex gravitational saddles.