Critical orthonormal Strichartz estimates for Lebesgue spaces

We study orthonormal Strichartz estimates at the critical coefficient exponent $q/2$ for fractional Schrödinger propagators. The proof for $d\geq3$ combines annular Schatten estimates with a frequency summation argument based on potential duality and Littlewood--Paley theory. In dimension two, a trace computation supplies the annular estimate needed for the global estimate. We also construct a counterexample to the global estimate with spatial $L^\infty$ and coefficients in $\ell^{q/2}$, even with a weak time norm.