Lifshitz holography: The whole shebang

We provide a general algorithm for constructing the holographic dictionary for any asymptotically locally Lifshitz background, with or without hyperscaling violation, and for any values of the dynamical exponents $z$ and $\theta$, as well as the vector hyperscaling violating exponent, that are compatible with the null energy condition. The analysis is carried out for a very general bottom up model of gravity coupled to a massive vector field and a dilaton with arbitrary scalar couplings. The solution of the radial Hamilton-Jacobi equation is obtained recursively in the form of a graded expansion in eigenfunctions of two commuting operators, which are the appropriate generalization of the dilatation operator for non scale invariant and Lorentz violating boundary conditions. The Fefferman-Graham expansions, the sources and 1-point functions of the dual operators, the Ward identities, as well as the local counterterms required for holographic renormalization all follow from this asymptotic solution of the radial Hamilton-Jacobi equation. We also find a family of exact backgrounds with $z>1$ and $\theta>0$ corresponding to a marginal deformation shifting the vector hyperscaling violating parameter and we present an example where the conformal anomaly contains the only $z=2$ conformal invariant in $d=2$ with four spatial derivatives.Comment: 83 pages, 1 figur

Holographic fluctuations and the principle of minimal complexity

We discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. We review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. We describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system.Comment: 10 pages, 4 figure

Generalized dilatation operator method for non-relativistic holography

We present a general algorithm for constructing the holographic dictionary for Lifshitz and hyperscaling violating Lifshitz backgrounds for any value of the dynamical exponent $z$ and any value of the hyperscaling violation parameter $\theta$ compatible with the null energy condition. The objective of the algorithm is the construction of the general asymptotic solution of the radial Hamilton-Jacobi equation subject to the desired boundary conditions, from which the full dictionary can be subsequently derived. Contrary to the relativistic case, we find that a fully covariant construction of the asymptotic solution for running non-relativistic theories necessitates an expansion in the eigenfunctions of two commuting operators instead of one. This provides a covariant but non-relativistic grading of the expansion, according to the number of time derivatives.Comment: 6 pages; v2 references added, discussion of the algorithm and the holographic dictionary improve

String effective actions, dualities, and generating solutions

This thesis covers in general two separate topics: the string e®ective actions and the geodesic motion of brane solutions. The main theme of the ¯rst topic, i.e., the string e®ective actions, is the construction of the abelian D-brane e®ective action. In the limit of constant ¯eld strengths this action is known as the Born-Infeld action. In this thesis we propose a new method for constraining the four dimensional D-brane e®ective action and applied to the abelian case with derivative corrections. The method is based on the electromagnetic duality invariance. We show that selfduality requirement only constrains the derivative corrections terms to the Born-Infeld theory but not determines them. In the second topic of this thesis we consider the geodesic motion on the symmetric moduli spaces that arise after timelike and spacelike reductions of (super)gravity theories. The geodesics correspond to timelike respectively spacelike p-brane solutions when they are lifted over a p-dimensional °at space. In particular, we consider the problem of constructing the minimal generating solution : a geodesic with the minimal number of free parameters such that all other geodesics are generated through isometries G: This way we ¯nd the most general °uxless Sp-brane solution of Einstein gravity with (deformed) worldvolume via the reduction over an Euclidean torus. In case we reduce over a Lorentzian torus, the target space becomes a pseudo-Riemannian G=H¤ with H¤ is a non-compact real form. Correspondingly, the geodesic solutions on G=H¤ are labeled by the sign of the a±ne velocity jjvjj2: We derive the generating solution for cosets GL(r + s)=SO(r; s); and give the Einstein vacuum solutions that can be obtained from uplifting a SL(n;R)=SO(n¡1; 1) stationary (¡1)-brane solution