The integrality gap of the Goemans--Linial SDP relaxation for Sparsest Cut is at least a constant multiple of $\sqrt{\log n}$

We prove that the integrality gap of the Goemans–Linial semidefinite programming relaxation for the Sparsest Cut Problem is $\mathrm{\Omega }(\sqrt{\log n})$ on inputs with $n$ vertices.