Vacuum condition and the relation between response parameter and anomaly coefficient in (1 + 3) dimensions

摘要

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}}_{4 d}=-8{pi}^2{c}_m ) between the response parameter (( {tilde{c}}_{4 d} )) 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