Gravity duals for non-relativistic CFTs

By K. Balasubramanian, John McGreevy. 2008

661 citations recorded by the source corpus.

We attempt to generalize the AdS/CFT correspondence to non-relativistic 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 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.

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

View Paper: https://www.semanticscholar.org/paper/7340f1fa7837bf91c1e6f91094d2f2e130e225fc

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Citations in the corpus

Quantum critical lines in holographic phases with (un)broken symmetry (2012, background): “The simplest example of this is Lifshitz scale symmetries, [3] and Schrödinger symmetries, [4] while more generic cases are theories with generalized Lifshitz invariance and hyperscaling violation, [1, 5, 6, 7] and the associated Schrödinger cousins [8].”
On Representations and Correlation Functions of Galilean Conformal Algebras (2009, background): “A gravity dual possessing these symmetries was then proposed in [9, 10] (see also [11, 12] for a somewhat different bulk realization).”
Carroll versus Galilei gravity (2017, background): “The AdS/CFT correspondence has been generalized to a non-relativistic correspondence where one considers gravitational background solutions in the bulk that preserve a number of non-relativistic symmetries such as the Schrödinger symmetries [4, 5] or Lifshitz symmetries [6].”
Holography for Schrödinger backgrounds (2010, background): “2); the fact that the scaling dimension depends on the lightcone momentum kv was noted previously in [1, 2, 15].”
AdS and Lifshitz black holes in conformal and Einstein-Weyl gravities (2012, methodology): “In a similar vein, D-dimensional geometries which exhibit Schrödinger symmetry are described by a metric of the form [40, 41]”
Aspects of holography for theories with hyperscaling violation (2012, background): “Very roughly speaking, in a theory with hyperscaling violation, the thermodynamic behaviour is as if the theory enjoyed dynamical exponent z but (1)An alternative class of non-relativistic scaling metrics characterizing the so-called Schrödinger spacetimes, which may also have condensed matter appli”
Galilean Conformal Algebras and AdS/CFT (2009, background): “A gravity dual possessing these symmetries was then proposed in [7, 8] (see also [9, 10] for a somewhat different bulk realisation).”
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”
Torsional Newton–Cartan geometry and the Schrödinger algebra (2014, background): “The holographic studies are building forth on attempts to extend the AdS/CFT correspondence to gravitational theories that can describe field theories that exhibit non-relativistic scale invariance (see [23, 24, 25, 26] and [27, 28, 29] for a review).”
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): “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.”
Consistent supersymmetric Kaluza-Klein truncations with massive modes (2009, background): “Starting with the work of [25][26] there has been some recent interest in constructing solutions of string/Mtheory that possess a non-relativistic conformal symmetry.”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, methodology): “Following this logic leads to the Schrödinger metric [306, 307],”
Quantum Gravity at a Lifshitz Point (2009, background): “Following [38, 39], 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”
On the coupling of Galilean-invariant field theories to curved spacetime (2014, background): “So the field theory duals to quantum gravity on Schrödinger spacetimes (see [4, 8]) naturally couple to NewtonCartan geometry with a Milne-invariant partition function.”