# Massless states on a compact manifold

I would like to understand the following statement found on page 6 second paragraph of 0305098.

The authors discuss the quantization of the level $k$ of the WZW model for compact (and non-compact) manifold. They notice that, on the compact case, $k$ is quantized and the (classical) tensionless limit is not valid anymore. That makes them quiet happy because:

This should not come as a surprise since massless particles on a compact manifold are problematic

Could someone give me a reference to understand this statement?

• I would imagine that massless particles and compact manifolds result to local gauge symmetry and that the problem would have to do with gauge fixing although I'm not sure if that's the reason. – Panos C. Jul 13 '18 at 12:20