Non-relativistic holography from Horava gravity

TL;DR

The paper constructs a comprehensive holographic framework for generic non-relativistic QFTs with conserved particle number by identifying NR electro-diffeomorphism symmetry with a bulk Horava gravity description. It develops two bulk realizations—via Kaluza-Klein vector khronons and via an Einstein-Maxwell NR limit—together with a robust holographic map that relates bulk fields to NR boundary sources, and it demonstrates NR conformal invariance in appropriate regimes. A key result is that NR two-point functions in conformal cases are fixed by symmetry and matched by the bulk construction, validating the duality. The work also outlines potential string theory embeddings and highlights avenues for exploring finite-Nc holography, quantum gravity aspects, and concrete NR systems such as quantum Hall states and unitary Fermi gases.

Abstract

Many non-relativistic Quantum Field Theories with conserved particle number share a common set of symmetries: time dependent spatial diffeomorphisms acting on the background metric and U(1) invariance acting on the background fields which couple to particle number. Here we use these symmetries to deduce a gravity dual for any such theory in terms of a non-relativistic theory of gravity, a variant of Horava gravity. This duality allows the extension of holography to generic non-relativistic field theories. As Horava gravity is presumed to be a consistent quantum theory, this duality also allows holography to move beyond the limit of a large number of colors, in principle. In the case when the field theory is conformally invariant, we prove that our proposal reproduces the form of the two point function demanded by this symmetry.