Gravity Duals for Nonrelativistic Conformal Field Theories

Abstract

We attempt to generalize the anti -de Sitter/conformal field theory correspondence to nonrelativistic conformal field theories which are invariant under Galilean transformations. Such systems govern ultracold atoms at unitarity, nucleon scattering in some channels, and, more generally, a family of universality classes of quantum critical behavior. We construct a family of metrics which realize these symmetries as isometries. They are solutions of gravity with a negative cosmological constant coupled to pressureless dust. We discuss realizations of the dust, which include a bulk superconductor. We develop the holographic dictionary and find two-point correlators of the correct form. A strange aspect of the correspondence is that the bulk geometry has two extra noncompact dimensions.

Non-relativistic holography from Hořava gravity

“…Preserving the trivial background under the temporal rescaling f = κt then requires the conformal transformation ω = −κ/z and the spatial rescaling ξ i = κx i /z, as expected for dynamical critical exponent z. It has been argued in [8], based on a holographic construction, that such scale and Galilean invariant fixed points should exist in interacting NR QFTs. In the action 2.2, as in Schrödinger's equation, m is a parameter, not a field.…”

“…Lacking perturbative tools to tackle these problems, there has recently been much interest in formulating holography for NR QFTs, starting with the work of [80,8]. In addition to the metric of GR, these works included a massive vector field in the gravitational theory.…”

The Brown-York mass of black holes in Warped Anti-de Sitter space

“…(54) Contributions to charges M = 2πρu i T * ij ξ j and J = 2πρu i T * iϕ coming from the large r expansions M ≃ M (1) r + M (0) + ... and J ≃ J (2) r 2 + J (1) where ρ (n) refer to the components of the large expansion of metric function (12) in powers of r; analogously for the large r expansion of u t = u t (0) + u t (−1) r −1 + u t (−2) r −2 , u ϕ ≃ u ϕ (−1) r −1 + u ϕ (−2) r −2 , and the Killing vectors ξ t = ξ t (0) = 1, ξ ϕ ≃ ξ ϕ (−1) r −1 + ξ ϕ (−2) r −2 . For the angular momentum, the analogous expression is J (2) 2π = ρ (1) Then, one finds that the mass of the black hole is given by M (0) while its angular momentum is given by J (0) .…”

“…This represents one of the most appealing attempts to generalize holography to non-AdS spaces, and this is because WAdS spaces appear in several contexts. For instance, WAdS spaces provide gravity duals for condensed matter systems with Schrödinger symmetry [12,13], they are closely related to the geometry of rotating black holes [14,15], and they also appear in relation to many other interesting subjects [16][17][18]. Asymptotically WAdS 3 spaces turn out to be exact solutions of String Theory [19][20][21][22][23] as well as of other models of threedimensional gravity, including Higher-Spin Gravity [24], Topologically Massive Gravity (TMG) [25,26], and New Massive Gravity (NMG) [27].…”

Minimal submanifolds asymptotic to AdS 4 × S 2 in AdS 5 × S 5

“…The AdS/CF T correspondence [1][2][3][4] has provided the physics community with an unique perspective in the attempt to understand the various phases of strongly coupled quantum field theory, and together with the probe-brane extension thereof [5][6][7], it has been providing the theoretical playground that renders possible toy-model building for a wide domain of interests, ranging from the quark-gluon plasma [8,9], unitary Fermi gas [10,11], to high-T c superconductor [12,13].…”