The role of Israel-Hartle-Hawking vacuum is discussed for anomalous fluid in presence of both the gauge and gravitational anomalies in ($1+3$) dimensions. I show that imposition of this vacuum condition leads to the relation $\tilde{ c}_{ 4d}=-8\pi^2c_m$ between the response parameter ($\tilde{ c}_{ 4d}$) and the anomaly coefficient ($c_m$). This establishes a connection between the coefficients appearing in a first order and a third order derivative terms in the constitutive relation.
Categories: gr-qc hep-th