Abstract
We derive quantum field theory Ward identities based on linear area preserving and conformal transformations in 2+1 dimensions. The identities relate Hall viscosities, Hall conductivities and the angular momentum. They apply both for relativistic and non relativistic systems, at zero and at finite temperature. We consider systems with or without translation invariance, and introduce an external magnetic field and viscous drag terms. A special case of the identities yields the well known relation between the Hall conductivity and half the angular momentum density.
Highlights
Quantum field theory Ward identities are relations among correlators that are derived using the symmetry generators
We derive quantum field theory Ward identities based on linear area preserving and conformal transformations in 2+1 dimensions
Ward identities introduce constraints among transport coefficients, which should be valid in holographic models that have quantum field theory dual descriptions
Summary
Quantum field theory Ward identities are relations among correlators that are derived using the symmetry generators. In [10] it has been shown that Ward identities of non-relativistic systems lead to a non-trivial relation between Hall viscosity and conductivities, and between Hall viscosity and angular momentum density. In this paper we will derive such identities for general relativistic or non-relativistic 2 + 1 dimensional quantum field theories, at zero and at finite temperature. For convenience we introduced in table 1 all the notations that will be used in the paper, and highlighted the main results in the different sections
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