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

Abstract

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 ${\tilde{c}}_{4d}=-8{\pi }^2{c}_m$ 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.

Comments added, to appear in JHEP

References in corpus (28)

• Hydrodynamics with Triangle Anomalies
• The Chiral Magnetic Effect and Anomaly-Induced Transport
• Gravitational Anomaly and Transport
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Constraints on Fluid Dynamics from Equilibrium Partition Functions
• Towards hydrodynamics without an entropy current
• Thermodynamics, gravitational anomalies and cones
• The chiral magnetic effect in hydrodynamical approach
• Conformal Nonlinear Fluid Dynamics from Gravity in Arbitrary Dimensions
• Connecting anomaly and tunneling methods for Hawking effect through chirality
• Notes on chiral hydrodynamics within effective theory approach
• Anomaly/Transport in an Ideal Weyl gas
• Anomaly inflow and thermal equilibrium
• Chern-Simons terms from thermal circles and anomalies
• Vacuum polarization in Schwarzschild space-time by anomaly induced effective actions
• Effective actions for anomalous hydrodynamics
• Constraints on Superfluid Hydrodynamics from Equilibrium Partition Functions
• Hawking Radiation, Covariant Boundary Conditions and Vacuum States
• Hydrodynamics in 1+1 dimensions with gravitational anomalies
• Anomalous charged fluids in 1+1d from equilibrium partition function
• Thermodynamics of Sultana-Dyer Black Hole
• Anomalous Transport in Holographic Chiral Superfluids via Kubo Formulae
• Two dimensional hydrodynamics with gauge and gravitational anomalies
• From Maxwell-Chern-Simons theory in $Ad{S}_3$ towards hydrodynamics in 1+1 dimensions
• Exact results in two dimensional chiral hydrodynamics with gravitational anomalies
• Parity odd equilibrium partition function in 2+1 dimensions
• Connection between response parameter and anomaly coefficient in two dimensional anomalous fluid
• Constitutive relations and response parameters in two dimensional hydrodynamics with gauge and gravitational anomalies

Cited by in corpus (6)

• Global Anomalies, Discrete Symmetries, and Hydrodynamic Effective Actions
• Anomalies and Entanglement Entropy
• Magnetoconductivity in chiral Lifshitz hydrodynamics
• Entropy current in two dimensional anomalous hydrodynamics and a bound on the sum of the response parameters
• Gravitational anomalies and one dimensional behaviour of black holes
• Thermal scalar field stress tensor on a two dimensional black hole and its near horizon properties