Heating up Galilean holography

Abstract

We embed a holographic description of a quantum field theory with Galilean conformal invariance in string theory. The key observation is that such field theories may be realized as conventional superconformal field theories with a known string theory embedding, twisted by the R-symmetry in a light-like direction. Using the Null Melvin Twist, we construct the appropriate dual geometry and its non-extremal generalization. From the nonzero temperature solution we determine the equation of state. We also discuss the hydrodynamic regime of these non-relativistic plasmas and show that the shear viscosity to entropy density ratio takes the universal value η/s = 1/4π typical of strongly interacting field theories with gravity duals. There are twists of the R-symmetry that preserve as many as 8 supercharges [23]. We use a simple twist which does not preserve any supersymmetry because of the resulting form of the H (3) flux. 4 We would like to thank Allan Adams for mentioning this DLCQ interpretation in informal discussion.

Non-relativistic holography from Hořava gravity

“…For d = 2 it is known that the field theory dual to the spacetime 3.19 is simply the discrete light cone quantization of N = 4 SYM theory in four spacetime dimensions [47,68]. Field theory properties, such as hydrodynamics and thermodynamics, follow from this relativistic reduction [47,75].…”

“…It is separately invariant under the symmetry transformations. It encodes the effect of R-twisted boundary conditions in the field theory [47,1,68]. To get a non-trivial field theory with the desired Schrödinger invariance twisting is not needed and the light-like circle compactification with periodic boundary conditions suffices.…”

“…The Null-Melvin Twist procedure of [47,1,68] used to generate the metric 3.19, including the additional r −4 Lifshitz term, is an infinite boost limit of this compactification, which once again can be interpreted as setting the chemical potential equal to the rest energy followed by a c → ∞ limit. …”

Transport properties of spacetime-filling branes

“…To name a few, holographic superconductivity was first constructed using a minimal set of matter fields and gravity [4], and only later string theory embeddings were studied [5][6][7]. The same happened for theories with Lifshitz or Schrödinger scaling, proposed in [8] and [9] respectively and then obtained from string theory in [10][11][12]. A different application of bottom-up models is a phenomenological approach.…”

Thermodynamics and gauge/gravity duality for Lifshitz black holes in the presence of exponential electrodynamics

“…For instance quantum Hall effect [3], fractional quantum Hall effect [4], Nernst effect [5][6][7] and superconductors [8][9][10][11][12] have been studied by this method. Furthermore, there are interesting strongly correlated electronic and atomic systems and also non-relativistic ones which possess Schrodinger symmetry [13][14][15]. Nevertheless, the near a critical point dynamics of such systems can be described by a relativistic conformal field theory or a more subtle scaling theory respecting the Lifshitz symmetry [16] t → λ z t, x → λ x.…”