Holographic stress tensor for non-relativistic theories

By S. Ross, Omid Saremi. 2009

178 citations recorded by the source corpus.

We discuss the calculation of the field theory stress tensor from the dual geometry for two recent proposals for gravity duals of non-relativistic conformal field theories. The first of these has a Schrodinger symmetry including Galilean boosts, while the second has just an anisotropic scale invariance (the Lifshitz case). For the Lifshitz case, we construct an appropriate action principle. We propose a definition of the non-relativistic stress tensor complex for the field theory as an appropriate variation of the action in both cases. In the Schrodinger case, we show that this gives physically reasonable results for a simple black hole solution and agrees with an earlier proposal to determine the stress tensor from the familiar AdS prescription. In the Lifshitz case, we solve the linearised equations of motion for a general perturbation around the background, showing that our stress tensor is finite on-shell.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/1f910914ae32e5e70878f667b0849e85615c40c7

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In Astronomy and Astrophysics

1. Marika Taylor
2. J. Hartong
3. N. Obers
4. S. Hartnoll
5. E. Kiritsis
6. E. Silverstein
7. John McGreevy
8. Jan Rosseel

In Nuclear and High Energy Physics

1. Marika Taylor
2. J. Hartong
3. S. Hartnoll
4. N. Obers
5. E. Kiritsis
6. John McGreevy
7. E. Silverstein
8. S. Sachdev

Citations in the corpus

• Lifshitz space–times for Schrödinger holography (2014, unknown): “The vielbein components of the energy–momentum tensor T ν correspond to energy density (T ντμv ), momentum flux (T ντμe a ), energy flux (T νeμv ) and stress (T νeμe b ), respectively (see also [11]).”
• Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography (2013, methodology): “Following [14] we call T tt (0) the energy density, T ti (0) the momentum T tt (0) T ti (0) T it (0) T ij (0) T b (0)a T a (0) scaling dimension 4 3 5 4 4 4”
• An analytic Lifshitz black hole (2009, background): “Recently, [28] have described an alternative set of boundary terms for asymptotically Lifshitz theories.”
• Towards strange metallic holography (2009, methodology): “Indeed such asymptotic behavior was found in the simple models of [42, 43], which used a massive vector field coupled to gravity.”
• Torsional Newton–Cartan geometry and the Schrödinger algebra (2014, methodology): “work [10] which showed the usefulness of Newton{Cartan geometry in the eective eld theory description of the quantum Hall eect and the work [11,12], building forth on earlier work [13,14,15,16] and [17,18,19,20,21,22], which showed that the boundary geometry of a specic class of asymptotically local”
• Holography for Schrödinger backgrounds (2010, background): “In other words, one should specify boundary conditions for the vielbein, rather than the metric; this point was noted in [18].”
• Lifshitz holography (2015, background): “The diffeomorphism Ward identity should follow from the momentum constraint, but this was not analysed in the vielbein approach in [113, 114].”