Schrödinger Invariance from Lifshitz Isometries in Holography and Field Theory

By J. Hartong, E. Kiritsis, N. Obers. 2014

142 citations recorded by the source corpus.

We study non-relativistic field theory coupled to a torsional Newton-Cartan geometry both directly as well as holographically. The latter involves gravity on asymptotically locally Lifshitz space-times. We define an energy-momentum tensor and a mass current and study the relation between conserved currents and conformal Killing vectors for flat Newton-Cartan backgrounds. It is shown that flat NC space-time realizes two copies of the Lifshitz algebra that together form a Schroedinger algebra (without the central element). We show why the Schroedinger scalar model has both copies as symmetries and the Lifshitz scalar model only one. Finally we discuss the holographic dual of this phenomenon by showing that the bulk Lifshitz space-time realizes the same two copies of the Lifshitz algebra.

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

View Paper: https://www.semanticscholar.org/paper/433f1754c0e44b5177ef0dc8ecd816d5bfb653fa

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In Astronomy and Astrophysics

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

In Nuclear and High Energy Physics

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

In Statistical and Nonlinear Physics

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

Citations in the corpus

• 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”
• Lifshitz space–times for Schrödinger holography (2014, background): “The notation among the papers [7, 8, 9] together with the current one is fully compatible.”
• On the coupling of Galilean-invariant field theories to curved spacetime (2014, background): “8), which amounts to a Newton-Cartan structure 8After this work was completed, two works appeared [29, 30] which argue that this boundary geometry is NC geometry in a similar sense to what we have described, and in particular there is a “hidden” Galilean boost symmetry.”