# Reply to "Comment on "Galilean invariance at quantum Hall edge""

## TL;DR

This paper revisits the conductivity of a Galilean-invariant quantum Hall edge, correcting previous calculations, aligning results with recent comments, and clarifying the non-universality of certain conductivity contributions.

## Contribution

It corrects earlier linear response calculations and refutes the universality of the shift-dependent contribution to longitudinal conductivity.

## Key findings

- Corrected the linear response calculation of conductivity.
- Aligned the model's results with recent comment findings.
- Demonstrated the non-universal nature of the shift contribution.

## Abstract

Motivated by a recent Comment by J. H\"oller and N. Read [Phys. Rev. B 93, 197401 (2016)], we revisit the problem of a chiral Luttinger liquid on a boundary of a Galilean-invariant quantum Hall fluid. After correcting the linear response calculation, the real part of the longitudinal conductivity derived in the model constructed in our paper [Phys. Rev. B 91, 195409 (2015)] agrees with the result found in the Comment for non-interacting fermions confined by a linear potential. We also withdraw our previous conjecture that the longitudinal conductivity contains a universal contribution determined by the "shift" and provide arguments demonstrating its non-universal nature.