Boundedness of BMN string entropy at strong coupling

Determine whether the BMN string entropy S_m(g), defined from the all-genus BMN two-point function probabilities p_{n,m}(g) in free N=4 SU(N) super Yang-Mills theory with coupling g = J^2/N, remains bounded or diverges as g tends to infinity.

Background

The authors define a physically motivated entropy generation process for BMN strings: starting from an initial basis state, the system evolves unitarily and a single measurement is performed in the BMN basis, producing a mixed state whose entropy depends on the all-genus transition probabilities p_{n,m}(g). At finite g, the entropy is finite.

Whether this entropy stays bounded as g→∞ is crucial for testing the proposed universal entropy bound in quantum gravity. If bounded, it would provide nontrivial evidence supporting the bound and potentially relate to the Gibbons-Hawking entropy scale.