The particle number in Galilean holography
Koushik Balasubramanian, John McGreevy
TL;DR
This work shows that the particle-number spectrum in Galilean holography need not arise from a compact ξ direction, by constructing bulk systems with asymptotic Schrödinger symmetry realized without the extra dimension. A lower-dimensional realization is achieved via dimensional reduction and a bulk gauge field that encodes particle-number symmetry, enabling finite-density solutions and an all-important M-theory lift that resolves curvature singularities. The authors identify a holographic Mott-insulator state at finite density, with a mass gap emerging from an IR lifting of the geometry, while translation invariance complicates the interpretation of transport properties. They further explore multi-species extensions and discuss implications for superfluid phases, signaling a rich landscape of Schrödinger holography beyond the original ξ-based constructions and offering a framework to study realistic spectra in NRCFT duals.
Abstract
Recently, gravity duals for certain Galilean-invariant conformal field theories have been constructed. In this paper, we point out that the spectrum of the particle number operator in the examples found so far is not a necessary consequence of the existence of a gravity dual. We record some progress towards more realistic spectra. In particular, we construct bulk systems with asymptotic Schrodinger symmetry and only one extra dimension. In examples, we find solutions which describe these Schrodinger-symmetric systems at finite density. A lift to M-theory is used to resolve a curvature singularity. As a happy byproduct of this analysis, we realize a state which could be called a holographic Mott insulator.