Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry

By D. Son. 2008

954 citations recorded by the source corpus.

We discuss a realization of the nonrelativistic conformal group (the Schr\"odinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field equations. We discuss various issues related to nonrelativistic holography. In particular, we argue that free fermions and fermions at unitarity correspond to the same bulk theory with different choices for the near-boundary asymptotics corresponding to the source and the expectation value of one operator. We describe an extended version of nonrelativistic general coordinate invariance which is realized holographically.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/982b57ab07f5960fcfba966e787f31a19c76e9e3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

Citations in the corpus

On the coupling of Galilean-invariant field theories to curved spacetime (2014, background): “ﬁned in a coordinate-independent way. The three major highlights of this development since [3] may be found in [4–6]. We also refer the reader to [16] for some applications of this machinery. In 2008 [4], Son ﬁrst wrote down his “general covariance” in terms of the action of inﬁnitesimal reparameter”
Quantum Gravity at a Lifshitz Point (2009, background): “Following [39, 40], a nonrelativistic version of the AdS/CFT correspondence has indeed received a lot of attention recently.”
Hot spacetimes for cold atoms (2008, background): “July 2008”
The Lovelock Black Holes (2008, methodology): “ﬁve-dimensional Lovelock gravity are considered, showing that higher-curvature corrections aﬀect the condensation phenomenon. Besides, the O(R2) corrections in the non-relativistic version of AdS/CFT [28, 27] were also studied, and the D = 5 Lovelock theory is also used in Ref. [26] as the working e”
Landscape of superconducting membranes (2009, background): “derstood. Note however that the AdS/CFT correspondence can be adapted to non-conformal relativistic theories (see e.g. [11] for a review) and also to theories with a non-relativistic scale invariance [12, 13, 14]. We will furthermore focus in this paper on 2+1 dimensional systems. The AdS/CFT corres”
Holographic Superconductors (2008, background): “The AdS/CFT correspondence has recently been generalised to non-relativistic theories [15, 16], and it would certainly be interesting to adapt our study to those cases.”
Holographic Quantum Matter (2016, background): “In [63; 678] a gravitational geometry was proposed as a dual to nonrelativistic CFTs.”
Introduction to holographic superconductor models (2015, background): “From a modern perspective, the correspondence is an equality between a quantum field theory (QFT) in d dimensional spacetime and a (4)The simple examples are Lifshitz symmetry [33] and Schrödinger symmetry [34, 35], while more generic cases are those with generalized Lifshitz invariance and hypersca”
The incompressible non-relativistic Navier-Stokes equation from gravity (2008, background): “of spatial conformal generators K i but does not include a generator that descends from the temporal conformal generator K0. Our algebra is distinct from the Schroedinger group studied for example in [15] – 3 – a reference frame whose velocity is homogeneous in space but an arbitrary function of tim”
Galilean Conformal Algebras and AdS/CFT (2009, methodology): “] that the Schrodinger symmetry group [3, 4], a non-relativistic version of conformal symmetry, is relevant to the study of cold atoms. A gravity dual possessing these symmetries was then proposed in [7, 8] (see also [9, 10] for a somewhat diﬀerent bulk realisation). Further developments along this ”
Lifshitz space–times for Schrödinger holography (2014, background): “…strongly coupled relativistic ﬁeld theories, there has been a growing interest in applying similar techniques to strongly coupled systems with non-relativistic symmetries [1–4 In this letter we show that, when applying holography to asymptotically locally Lifshitz space–times, the resulting”
Lifshitz solutions of D=10 and D=11 supergravity (2010, background): “In the second approach, one instead considers a Schrödinger(z) geometry of the form [3][4]:”
Holographic Duality with a View Toward Many-Body Physics (2009, background): “Other examples include systems which in the UV are described by non-relativistic CFTs, as described in [17, 18, 16].”
Lifshitz black hole in three dimensions (2009, background): “[3, 4], spacetimes whose isometry group is the so-called Schrödinger group were proposed to be gravity duals for Galilean and scale invariant systems.”
Kerr/CFT Correspondence (2008, background): “lassical solutions. In the last few years we are beginning to see interesting applications of holographic duality outside of string theory in nuclear [5, 6, 7], condensed matter [8, 9, 10] and atomic [11, 12] physics. 1 Oddly, the rich ideas surrounding holographic dualities so far have not been suc”