Effective boundary theory of the quantized thermal Hall effect

We study the effective gravitational field theory that accounts for the quantized thermal Hall effect. The effective theory is microscopically derived from the one-dimensional massless boundary fermion, which is a manifestation of the two-dimensional bulk Dirac fermion with nontrivial energy band topology. The gravitational response of the boundary effective theory explains the bulk quantized thermal Hall effect through the Str\v{e}da formula.