Entanglement, anomalies and Mathisson's helices

Abstract

We study the physical properties of a length-torsion functional which encodes the holographic entanglement entropy for 1+1 dimensional theories with chiral anomalies. Previously, we have shown that its extremal curves correspond to the mysterious Mathisson's helical motions for the centroids of spinning bodies. We explore the properties of these helices in domain-wall backgrounds using both analytic and numerical techniques. Using these insights we derive an entropic $c$-function $c_{\mathrm{Hel}}(\ell)$ which can be succinctly expressed in terms of Noether charges conserved along these helical motions. While for generic values of the anomaly there is some ambiguity in the definition of $c_{\mathrm{Hel}}(\ell)$, we argue that at the chiral point this ambiguity is absent.