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.
Murthy,The growth of the1/16-bps index in 4dN= 4SYM,Phys
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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.
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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.