Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography

By M. Christensen, J. Hartong, N. Obers, B. Rollier. Journal of High Energy Physics, 2013

230 citations recorded by the source corpus.

For a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions.

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

View Paper: https://www.semanticscholar.org/paper/6769bd92a16dec9c548cb369f801fa90bd6acf43

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Citations in the corpus

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.”
On the coupling of Galilean-invariant field theories to curved spacetime (2014, result): “7Our results have some overlap with those of [7,20] and especially [16].”
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”
Carroll versus Galilei gravity (2017, background): “28) means that this geometry has twistless torsion [26].”
Torsional Newton–Cartan geometry and the Schrödinger algebra (2014, methodology): “In the ≠ z 2 case, we will also ﬁ nd that the simple gauging of the Schrödinger algebra leads to an extra ﬁ eld, not present in the description of TNC geometry of [11, 12].”
Hořava-Lifshitz gravity from dynamical Newton-Cartan geometry (2015, methodology): “The benefit of adding torsion to the formalism was first considered in [17, 18] including the case with no constraint on τμ.”