Quantum Gravity at a Lifshitz Point

By Petr Hořava. 2009

2,455 citations recorded by the source corpus.

We present a candidate quantum field theory of gravity with dynamical critical exponent equal to $z=3$ in the UV. (As in condensed-matter systems, $z$ measures the degree of anisotropy between space and time.) This theory, which at short distances describes interacting nonrelativistic gravitons, is power-counting renormalizable in $3+1$ dimensions. When restricted to satisfy the condition of detailed balance, this theory is intimately related to topologically massive gravity in three dimensions, and the geometry of the Cotton tensor. At long distances, this theory flows naturally to the relativistic value $z=1$, and could therefore serve as a possible candidate for a UV completion of Einstein's general relativity or an infrared modification thereof. The effective speed of light, the Newton constant and the cosmological constant all emerge from relevant deformations of the deeply nonrelativistic $z=3$ theory at short distances.

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

View Paper: https://www.semanticscholar.org/paper/94263373aab6f312e32722646a07806e05c992c5

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Citations in the corpus

Strong coupling in Horava gravity (2009, methodology): “Indeed, note that the last of these transformations shows that if N is restricted to be ”projectable” [2], i.”
On the coupling of Galilean-invariant field theories to curved spacetime (2014, background): “Recently, it was claimed [24, 25] on symmetry grounds that Horava-Lifshitz gravity [26] on spacetimes with certain asymptotics is holographically dual to some Galilean-invariant field theories.”
Effective field theory of dark energy: A review (2019, background): “• Low-energy Hořava gravity [46, 259]: Hořava gravity is considered a candidate for the ultra-violet completion of GR [46, 259].”
Dark Energy in Light of Multi-Messenger Gravitational-Wave Astronomy (2018, background): “A typical example of a Lorentz-violating theory would be high-energy Hořava gravity (Horava, 2009) in which”
Einstein gravity as a 3D conformally invariant theory (2010, background): “Recently, spatial conformal symmetry has played an important role in quantum gravity both through Hořava’s proposal [7] for a UV completion of general relativity and Maldecena’s AdS/CFT conjecture [8].”
Nonperturbative quantum gravity (2012, background): “They are asymmetric in space and time in the sense that higher-derivative terms appear, but only in the form of spatial derivatives [26].”
Quantum-Spacetime Phenomenology (2008, background): “The study of Planck-scale departures from Lorentz symmetry may find some encouragement in perspectives based on renormalization theory, at least in as much as it has been shown [79, 78, 289, 507] that some field theories modified by Lorentz-violating terms are actually rather well behaved in the UV.”
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, background): “In the search for consistent theories of quantum gravity, Hořava-Lifshitz (HL) gravity [1, 2] has appeared as a tantalizing possibility of a non-Lorentz invariant and renormalizable UV completion of gravity.”
A consistent theory of D → 4 Einstein-Gauss-Bonnet gravity (2020, neutral): “[27] P.”
Science with the space-based interferometer LISA. IV: probing inflation with gravitational waves (2016, background): “Horava-Lifshitz scenarios [138], the Higuchi bound does not necessarily apply.”
Modified Gravity and Cosmology (2011, background): “To reduce the number of terms, Hořava originally borrowed the notion of detailed balance from condensed matter theory [619], but this has since been shown to lead to phenomenological problems [278, 1169, 1170].”
Dust of dark energy (2010, background): “[18] on caustics in the ghost condensate [19] and the discussion in Refs [20, 21] on caustics in Hořava gravity [22].”
Lifshitz space–times for Schrödinger holography (2014, background): “Is that only true for Einstein gravity coupled to a bulk vector field? For example what would happen7 in the context of Horava–Lifshitz gravity/Einstein-aether theories [42,43]? The Schrödinger algebra has an infinite extension in the form of the Schödinger–Virasoro algebra, it would be interesting ”