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.
Counting BPS operators in N=4 SYM
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The free field partition function for a generic U(N) gauge theory, where the fundamental fields transform in the adjoint representation, is analysed in terms of symmetric polynomial techniques. It is shown by these means how this is related to the cycle polynomial for the symmetric group and how the large N result may be easily recovered. Higher order corrections for finite N are also discussed in terms of symmetric group characters. For finite N, the partition function involving a single bosonic fundamental field is recovered and explicit counting of multi-trace quarter BPS operators in free \N=4 super Yang Mills discussed, including a general result for large N. The partition function for BPS operators in the chiral ring of \N=4 super Yang Mills is analysed in terms of plane partitions. Asymptotic counting of BPS primary operators with differing R-symmetry charges is discussed in both free \N=4 super Yang Mills and in the chiral ring. Also, general and explicit expressions are derived for SU(2) gauge theory partition functions, when the fundamental fields transform in the adjoint, for free field theory.
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In SO(d)- and O(d)-invariant sectors of the U(N) d-matrix harmonic oscillator, microcanonical heat capacity is negative at low energy and turns positive at kcrit ~ N^2/4, producing a caloric fold analogous to AdS black holes.
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.
citing papers explorer
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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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Negative heat capacities in spherically symmetric sectors of $d$-matrix quantum mechanics
In SO(d)- and O(d)-invariant sectors of the U(N) d-matrix harmonic oscillator, microcanonical heat capacity is negative at low energy and turns positive at kcrit ~ N^2/4, producing a caloric fold analogous to AdS black holes.
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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.