A Comment on Holographic Luttinger Theorem

TL;DR

This paper investigates the robustness of the holographic Luttinger theorem under various deformations of the gravity dual, confirming its validity in confining phases and identifying universal charge deficits in deconfined phases.

Contribution

It demonstrates that the holographic Luttinger theorem remains valid under multiple deformations in confining phases and reveals universal charge deficits in deconfined phases.

Findings

Luttinger theorem holds in confining phases despite deformations.

Universal charge deficit measures deconfined fermion charge.

Deformations do not violate the holographic derivation of the theorem.

Abstract

Robustness of the Luttinger theorem for fermionic liquids is examined in holography. The statement of the Luttinger theorem, the equality between the fermion charge density and the volume enclosed by the Fermi surface, can be mapped to a Gauss's law in the gravity dual, a la Sachdev. We show that various deformations in the gravity dual, such as inclusion of magnetic fields, a parity-violating theta-term, dilatonic deformations, and higher-derivative corrections, do not violate the holographic derivation of the Luttinger theorem, as long as the theory is in a confining phase. Therefore a robustness of the theorem is found for strongly correlated fermions coupled with strongly coupled sectors which admit gravity duals. On the other hand, in the deconfined phase, we also show that the deficit appearing in the Luttinger theorem is again universal. It measures a total deficit which measures the charge of the deconfined ("fractionalized") fermions, independent of the deformation parameters.