Conformal perturbation theory

Statistical systems near a classical critical point have been intensively studied both from theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the experimental data of real systems. In order to compute physical quantities near a critical point one needs to know the model at the critical (conformal) point. In this line, recent progresses in the knowledge of conformal field theories, through the conformal bootstrap, give the hope to get some interesting results also outside of the critical point. In this note we will review and clarify how, starting from the knowledge of the critical correlators, one can calculate in a safe way their behavior outside the critical point. The approach illustrated requires the model to be just scale invariant at the critical point. We will clarify the method by applying it to different kind of perturbations of the $2D$ Ising model.Comment: 21 pages, Version to appear on PR

Magneto-transport from momentum dissipating holography

We obtain explicit expressions for the thermoelectric transport coefficients of a strongly coupled, planar medium in the presence of an orthogonal magnetic field and momentum-dissipating processes. The computations are performed within the gauge/gravity framework where the momentum dissipation mechanism is introduced by including a mass term for the bulk graviton. Relying on the structure of the computed transport coefficients and promoting the parameters to become dynamical functions, we propose a holography inspired phenomenology open to a direct comparison with experimental data from the cuprates.Comment: 23 page

Holography in flat spacetime: 4D theories and electromagnetic duality on the border

We consider a free topological model in 5D euclidean flat spacetime, built from two rank-2 tensor fields. Despite the fact that the bulk of the model does not have any particular physical interpretation, on its 4D planar edge nontrivial gauge field theories are recovered, whose features are entirely determined by the gauge and discrete symmetries of the bulk. In particular no 4D dynamics can be obtained without imposing a Time Reversal invariance in the bulk. Remarkably, one of the two possible edge models selected by the Time Reversal symmetries displays a true electromagnetic duality, which relates strong and weak coupling regimes. Moreover this same model, when considered on-shell, coincides with the Maxwell theory, which therefore can be thought of as a 4D boundary theory of a seemingly harmless 5D topological model.Comment: 21 pages, plain LaTeX, no figures. Version to appear on JHE

Analytic DC thermo-electric conductivities in holography with massive gravitons

We provide an analytical derivation of the thermo-electric transport coefficients of the simplest momentum-dissipating model in gauge/gravity where the lack of momentum conservation is realized by means of explicit graviton mass in the bulk. We rely on the procedure recently described by Donos and Gauntlett in the context of Q-lattices and holographic models where momentum dissipation is realized through non-trivial scalars. The analytical approach confirms the results found previously by means of numerical computations.Comment: 9 pages, no figures, minor comments added, version to appear on PR

Chasing the cuprates with dilatonic dyons

Magnetic field and momentum dissipation are key ingredients in describing condensed matter systems. We include them in gauge/gravity and systematically explore the bottom-up panorama of holographic IR effective field theories based on bulk Einstein-Maxwell Lagrangians plus scalars. The class of solutions here examined appear insufficient to capture the phenomenology of charge transport in the cuprates. We analyze in particular the temperature scaling of the resistivity and of the Hall angle. Keeping an open attitude, we illustrate weak and strong points of the approach.Comment: 30 pages, 2 figures, Version to appear in JHE

A holographic perspective on phonons and pseudo-phonons

We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic Q-lattice, provides a privileged setup to study the emergence of phonons from a spontaneous translational symmetry breaking in a conformal field theory and offers valuable hints for the treatment of phonons in QFT at large. We first analyze the Ward identity structure by means of standard QFT techniques, considering both spontaneous and explicit symmetry breaking. Next, by implementing holographic renormalization, we show that the same set of Ward identities holds in the holographic Q-lattice. Eventually, relying on the holographic and QFT results, we study the correlators realizing the symmetry breaking pattern and how they encode information about the low-energy spectrum.Comment: 31+1 pages, version accepted on JHE

Thermo-electric transport in gauge/gravity models

In this review, we summarize recent results in the study of the thermo-electric transport properties of holographic models exhibiting mechanism of momentum dissipation. These models are of particular interests if applied to understand the transport mechanisms of strongly coupled condensed matter systems such as the high-temperature superconductors. After a brief introduction in which we point out the discrepancies between the experimentally measured transport properties of these materials and the prediction of the weakly coupled theory of Fermi Liquid, we will review the basic aspects of AdS/CFT correspondence and how gravitational models could help in understanding the peculiar properties of strongly coupled condensed matter systems

Bounds on charge and heat diffusivities in momentum dissipating holography

Abstract: Inspired by a recently conjectured universal bound for thermo-electric diffusion constants in quantum critical, strongly coupled systems and relying on holographic analytical computations, we investigate the possibility of formulating Planckian bounds in different holographic models featuring momentum dissipation. For a certain family of solutions to a simple massive gravity dilaton model at zero charge density we find linear in temperature resistivity and entropy density alongside a constant electric susceptibility. In addition we explicitly find that the sum of the thermo-electric diffusion constants is bounded

Leading order magnetic field dependence of conductivities in anomalous hydrodynamics

We show that literature results claimed for the magnetic field dependence of the longitudinal conductivity in anomalous first-order hydrodynamics are frame dependent at this derivative order. In particular, we focus on $(3+1)$-dimensional hydrodynamics in the presence of a constant ${\cal O}(\partial)$ magnetic field with a $U(1)$ chiral anomaly and demonstrate that, for constitutive relations up to and including order one in derivatives, the anomaly drops out of the longitudinal conductivity. In particular, magnetic field dependent terms that were previously found in the literature only enter the non-zero frequency thermoelectric conductivities through explicitly frame dependent pieces indicating that they are not physical. This issue can be avoided entirely by incorporating the magnetic field into the fluid's equilibrium state.Comment: V2: Several Clarifications added, title changed, Version to appear on Physical review