Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry

By J. Hartong, N. Obers. Journal of High Energy Physics, 2015

161 citations recorded by the source corpus.

Recently it has been established that torsional Newton-Cartan (TNC) geometry is the appropriate geometrical framework to which non-relativistic field theories couple. We show that when these geometries are made dynamical they give rise to Hořava-Lifshitz (HL) gravity. Projectable HL gravity corresponds to dynamical Newton-Cartan (NC) geometry without torsion and non-projectable HL gravity corresponds to dynamical NC geometry with twistless torsion (hypersurface orthogonal foliation). We build a precise dictionary relating all fields (including the scalar khronon), their transformations and other properties in both HL gravity and dynamical TNC geometry. We use TNC invariance to construct the effective action for dynamical twistless torsional Newton-Cartan geometries in 2+1 dimensions for dynamical exponent 1 < z ≤ 2 and demonstrate that this exactly agrees with the most general forms of the HL actions constructed in the literature. Further, we identify the origin of the U(1) symmetry observed by Hořava and Melby-Thompson as coming from the Bargmann extension of the local Galilean algebra that acts on the tangent space to TNC geometries. We argue that TNC geometry, which is manifestly diffeomorphism covariant, is a natural geometrical framework underlying HL gravity and discuss some of its implications.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8c413d2aec4274622112e8d9ccb42eef42eedc62

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In Astronomy and Astrophysics

1. J. Hartong
2. N. Obers
3. Marika Taylor
4. Ziqi Yan
5. Anzhong Wang
6. T. Harmark
7. Lorenzo Menculini
8. Eric Bergshoeff

In Nuclear and High Energy Physics

1. J. Hartong
2. N. Obers
3. Marika Taylor
4. Ziqi Yan
5. Anzhong Wang
6. T. Harmark
7. Lorenzo Menculini
8. E. Kiritsis

Citations in the corpus

• Strings with non-relativistic conformal symmetry and limits of the AdS/CFT correspondence (2018, methodology): “This is analogous to the way that gauging the Bargmann algebra (massive Galilei algebra) gives TNC geometry [13, 28].”
• Lifshitz holography (2015, background): “This question has been explored recently in a number of studies, see [127, 137, 138].”
• Hořava gravity at a Lifshitz point: A progress report (2017, background): “20 Recently, another important discovery of the nonrelativistic gauge/gravity duality is the one-to-one correspondence between the Hořava gravity with the enlarged symmetry (2.34) and the Newton-Cartan geometry (NCG) [145].”