Citation: Kapustin, Anton, and Lev Spodyneiko. "Absence of energy currents in an equilibrium state and chiral anomalies." Physical review letters 123.6 (2019): 060601.
Web: https://arxiv.org/abs/1904.05491
Tags: Generalized-symmetries, Conformal-field-theory
The results from this paper are great, but I find it a little confusing. What I find much easier to understand is the description of this paper in
> Kapustin, Anton, and Lev Spodyneiko. "Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems." Physical Review B 101.4 (2020): 045137.
Kapustin and Spodyneiko say that the results of the present paper are as follows: "the chiral central charge of the edge modes (and more generally, the equilibrium energy current carried by the edge modes) is independent of the particular edge. Hence the low-temperature thermal Hall conductivity of a gapped 2d material defined via [the chiral central charge of the edge] is a well-defined bulk property". Moreover, the results of the present paper show that the chiral central charge of the edge modes do not vary as the paramaters of the Hamiltonian are tuned without a gap closing.
This is a fantastic result. The chiral central charge is quite hard to define as a bulk invariant, so you like to define it via the boundary. However, it is not at all immediately clear that the chiral central charge is independent of the choice of boundary theory! It is nice to know that such an argument exists.