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We show that the Goemans-Linial semidefinite relaxation of the Sparsest Cutproblem with general demands has integrality gap $(\log n)^{\Omega(1)}$. Thisis achieved by exhibiting $n$-point metric spaces of negative type whose $L_1$distortion is $(\log n)^{\Omega(1)}$. Our result is based on quantitativebounds on the rate of degeneration of Lipschitz maps from the Heisenberg groupto $L_1$ when restricted to cosets of the center.

A $(\log n)^{\Omega(1)}$ integrality gap for the Sparsest Cut SDP