Related papers: Lifshitz holography: The whole shebang
We study holographic renormalization and the variational problem in four-dimensional Einstein gravity coupled to a self-interacting scalar field in asymptotically AdS spacetimes with mixed, designer-gravity boundary conditions. For static…
We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly…
Deformation of any d-dimensional conformal field theory by a constant null source for a vector operator of dimension (d + z -1) is exactly marginal with respect to anisotropic scale invariance, of dynamical exponent z. The holographic duals…
Having in mind extensions of 2D holography beyond the Jackiw-Teitelboim model we propose holographic counterterms and asymptotic conditions for a family of asymptotically AdS$_2$ dilaton gravity models leading to a consistent variational…
Just like AdS spacetimes, Lifshitz spacetimes require counterterms in order to make the on-shell value of the bulk action finite. We study these counterterms using the Hamilton-Jacobi method. Rather than imposing boundary conditions from…
In this work, a minisuperspace model for the projectable Ho\v{r}ava-Lifshitz (HL) gravity without the detailed balance condition is investigated. The Wheeler-deWitt equation is derived and its solutions are studied and discussed for some…
Horava gravity theory possesses global Lifshitz space as a solution and has been conjectured to provide a natural framework for Lifshitz holography. We derive the conditions on the two derivative Horava gravity Lagrangian that are necessary…
Horava's "Lifschitz point gravity" has many desirable features, but in its original incarnation one is forced to accept a non-zero cosmological constant of the wrong sign to be compatible with observation. We develop an extension of…
We show that the IR action of the healthy non-projectable Ho\v{r}ava-Lifshitz (HL) gravity and its small modification exhibit asymptotically Lifshitz and hyperscaling violating solutions, respectively. The model may also have an…
Functional Hamilton-Jacobi (HJ) equation, the central equation of the holographic renormalization group (HRG), functional Schr\"{o}dinger equation, and generalized Wilson-Polchinski (WP) equation, the central equation of the functional…
We examine Hamilton-Jacobi equations driven by fully nonlinear degenerate elliptic operators in the presence of superlinear Hamiltonians. By exploring the Ishii-Jensen inequality, we prove that viscosity solutions are locally…
The 2+1 dimensional quantum Lifshitz model can be generalised to a class of higher dimensional free field theories that exhibit Lifshitz scaling. When the dynamical critical exponent equals the number of spatial dimensions, equal time…
We consider holography for Lifshitz spacetimes with dynamical exponent z=1+epsilon^2, where epsilon is small. We show that the holographically dual field theory is a specific deformation of the relativistic CFT, corresponding to the z=1…
An algebraic Riccati equation for linear operators is studied, which arises in systems theory. For the case that all involved operators are unbounded, the existence of infinitely many selfadjoint solutions is shown. To this end, invariant…
We investigate the holographic renormalization of the Einstein-Maxwell-dilaton theory which provides an asymptotic Lifshitz geometry dual to a Lifshitz field theory. In this case, the existence of a field combination with zero scaling…
We develop a general framework for computing the holographic 2-point functions and the corresponding conductivities in asymptotically locally AdS backgrounds with an electric charge density, a constant magentic field, and possibly…
In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator…
We investigate deformations of Gauss-Bonnet-Lifshitz holography in $(n+1)$ dimensional spacetime. Marginally relevant operators are dynamically generated by a momentum scale $\Lambda \sim 0$ and correspond to slightly deformed…
We study in detail a variety of gravitational toy models for hyperscaling-violating Lifshitz (hvLif) space-times. These space-times have been recently explored as holographic dual models for condensed matter systems. We start by considering…
We investigate deformations of Lifshitz holography in $(n+1)$ dimensional spacetime. After discussing the situation for general Lifshitz scaling symmetry parameter $z$, we consider $z=n-1$ and the associated marginally relevant operators.…