Torsional Newton-Cartan geometry and Lifshitz holography

By M. Christensen, J. Hartong, N. Obers, B. Rollier. 2013

270 citations recorded by the source corpus.

We obtain the Lifshitz UV completion in a specific model for z=2 Lifshitz geometries. We use a vielbein formalism which enables identification of all the sources as leading components of well-chosen bulk fields. We show that the geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry with a specific torsion tensor. We explicitly compute all the vacuum expectation values (VEVs) including the boundary stress-energy tensor and their Ward identities. After using local symmetries or Ward identities the system exhibits 6+6 sources and VEVs. The Fefferman-Graham expansion exhibits, however, an additional free function which is related to an irrelevant operator whose source has been turned off. We show that this is related to a second UV completion.

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

View Paper: https://www.semanticscholar.org/paper/4fe9fe8c94bdece7cbf6b17225c4111ced050832

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Citations in the corpus

Lifshitz holography (2015, methodology): “Newton–Cartan structure in holographic models Following on from the work of [133], further analysis of the reduced axion-dilaton model has indicated that the dual field theories couple to torsionful Newton–Cartan geometry [123, 135].”
Spacetime symmetries of the quantum Hall effect (2014, background): “[29] so that connection on these slices is the usual, torsionless Riemannian connection.”
Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography (2013, methodology): “Using this philosophy, we have presented in [39] the basic ingredients of an explicit holographic dictionary for Lifshitz holography at the level of the supergravity approximation.”
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, methodology): “(3)These three cases also naturally arise in Lifshitz holography [17, 18].”
Gauging the Carroll algebra and ultra-relativistic gravity (2015, methodology): “Similar gauging techniques also allow one to describe torsional Newton-Cartan (TNC) geometry which was found in a holographic context in [1, 3, 16, 17].”
Torsional Newton–Cartan geometry and the Schrödinger algebra (2014, methodology): “In [11, 12] this formalism was applied to identify which boundary values of (1)We refer to [3, 4, 5, 6, 7, 8, 9] for earlier work on Newton–Cartan geometry.”
Lifshitz space–times for Schrödinger holography (2014, methodology): “Our development builds on the recent works [5,6] in which, for a specific action supporting z = 2 Lifshitz geometries, the Lifshitz UV completion was identified by solving for the most general solution near the Lifshitz boundary.”
Strings with non-relativistic conformal symmetry and limits of the AdS/CFT correspondence (2018, methodology): “The approach taken was to first consider a target space null reduction of the relativistic Polyakov action with fixed momentum of the string along the null isometry, leading to a covariant action for strings moving in a torsional Newton–Cartan (TNC) geometry2 [6–13] after a Legendre transform that p”