Density-curvature response and gravitational anomaly
  We study constraints imposed by the Galilean invariance on linear electromagnetic and elastic responses of two-dimensional gapped systems in background magnetic field. Exact relations between response functions following from the Ward identities are derived. In addition to viscosity-conductivity relations known in literature we find new relations between the density-curvature response and the chiral central charge. 
Andrey Gromov, Alexander G. Abanov
cond-mat.str-el cond-mat.mes-hall hep-th math-ph math.MP