Sigma 35mm F1.4 DG HSM "Art"
Distortion
The Sigma 35mm F1.4 has negligible barrel distortion on APS-C. The only danger with this lens is perspective distortion: when shooting portraits or other subjects at close distances, distortion may be introduced due to the proximity of the lens to your subject. This applies to any wide-angle lens used for close-ups and can be used to your advantage if you're aware of its presence.
At a distance of approximately 5 meters and onward, there is no distortion to speak of in practice, as evidenced by the brick wall test photo below: