Gravity Duals of Lifshitz-Like Fixed Points

By S. Kachru, Xiao Liu, Michael Mulligan. 2008

1,114 citations recorded by the source corpus.

We find candidate macroscopic gravity duals for scale-invariant but non-Lorentz invariant fixed points, which do not have particle number as a conserved quantity. We compute two-point correlation functions which exhibit novel behavior relative to their AdS counterparts, and find holographic renormalization group flows to conformal field theories. Our theories are characterized by a dynamical critical exponent z, which governs the anisotropy between spatial and temporal scaling t {yields} {lambda}{sup z}t, x {yields} {lambda}x; we focus on the case with z = 2. Such theories describe multicritical points in certain magnetic materials and liquid crystals, and have been shown to arise at quantum critical points in toy models of the cuprate superconductors. This work can be considered a small step towards making useful dual descriptions of such critical points.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/af1ae1bc8558cd0922f3d77f938180fa175cc958

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Citations in the corpus

Lectures on holographic non-Fermi liquids and quantum phase transitions (2011, background): “29 Note that at this “singularity” all scalar curvature invariants are actually finite, but nevertheless an observer freely falling into the singularity will feel divergent tidal forces [105].”
Holographic c-theorems in arbitrary dimensions (2010, background): “Models with Schrödinger [84] and Lifshitz [85] symmetries have been studied and further the contribution of higher curvature terms has also been considered in this context [86].”
Landscape of superconducting membranes (2009, background): “[11] for a review) and also to theories with a non-relativistic scale invariance [12, 13, 14].”
Lifshitz scaling and hyperscaling violation in string theory (2012, background): “Effective gravity theories with abelian gauge fields as well as scalar fields [3, 4, 20, 21, 22, 23, 24, 25, 26, 27] are in fact quite rich, and have been shown to contain larger classes of solutions exhibiting interesting scaling properties.”
Black holes in asymptotically Lifshitz spacetime (2008, methodology): “In the present paper we develop further a recently proposed gravitational dual description [15] of a class of critical phenomena exhibiting unconventional scaling of the form t→ λt, x→ λx, (1) with z 6= 1.”
Lifshitz spacetimes from AdS null and cosmological solutions (2010, methodology): “For a massless bulk scalar, we have ∆ = 4, recovering the equal time 2-point function of the (2+1)-dim Lifshitz theory of [8]: it also corroborates the expectation [33] that the equal time correlators of this (2+1)-dim Lifshitz theory are identical to those of a 2-dim Euclidean conformal field theor”
Strongly correlated quantum fluids: ultracold quantum gases, quantum chromodynamic plasmas and holographic duality (2012, background): “, [305–308] and references therein).”
What Can Gauge-Gravity Duality Teach Us about Condensed Matter Physics? (2011, background): “It has become the practice in the string theory literature to call this the ‘Lifshitz’ metric [87] (for not particularly good reasons).”
Field theory at a Lifshitz point (2009, background): “eory is just classically scale invariant and may not be scale invariant quantum mechanically. Obviously a careful investigation of RG ﬂow and quantum criticality would be a very interesting issue. In [24], the gravity duals of the anisotropic scale invariant ﬁeld theory have been constructed. It wou”
Holography of charged dilaton black holes (2009, background): “The scaling exponents that characterize the solution actually indicate that in the near-horizon region, the metric takes the form characterizing a Lifshitz fixed point with anisotropic scaling [26] (see also [27]).”
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography (2013, background): “By far the majority of work on Lifshitz holography has been within the context of the massive vector model [4, 5] because it is simple in matter content and because it can account for all values of z by suitably choosing the cosmological constant and mass parameter.”
Holographic stress tensor for non-relativistic theories (2009, methodology): “In [18], it was proposed that a holographic dual to a theory with the anisotropic scaling symmetry (1.”
Thermodynamics and instabilities of a strongly coupled anisotropic plasma (2011, background): “Nevertheless, as pointed out in [121] and elaborated upon in [122], the hypersurface r = 0 is still problematic because tidal forces become infinite as this hypersurface is approached.”
An analytic Lifshitz black hole (2009, methodology): “Interestingly, these are solutions to precisely the system studied by [8], with no additional fields.”
Universal diffusion in incoherent black holes (2016, background): “They correspond to the well-studied class of metrics known as hyperscaling violating geometries [27–32].”