The stability properties of a family of magnetic AdS 3 ×R 2 solutions of D = 5, SO(6) gauged SUGRA are investigated in more detail. We construct an analogous family of magnetic AdS 2 × R 2 solutions of D = 4, SO (8) gauged SUGRA, including a family of supersymmetric solutions, and also investigate their stability. We construct supersymmetric domain walls that interpolate between AdS 5 and an AdS 3 ×R 2 solution and also between AdS 4 and an AdS 2 × R 2 solution which provide stable zero temperature ground states for the corresponding dual CFTs. We also construct new families of electric AdS 2 × R 3 and AdS 2 × R 2 solutions.

We investigate spatially modulated instabilities of magnetically charged $AdS_{2}\times\mathbb{R}^2$, $AdS_{3}\times\mathbb{R}^2$ and $AdS_{2}\times\mathbb{R}^3$ backgrounds in a broad class of theories, including those arising from KK reductions of ten and eleven dimensional supergravity. We show that magnetically charged black brane solutions in D=4,5 spacetime dimensions, whose zero temperature near horizon limit approach these backgrounds, can have instabilities that are dual to phases with current density waves that spontaneously break translation symmetry. Our examples include spatially modulated instabilities for a new class of magnetic black brane solutions of D=5 SO(6) gauged supergravity, that we construct in closed form, which are dual to new phases of N=4 SYM theory.Comment: 21 pages, 2 figures. Very minor typos fixed. Version published in JHE

We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength deformations of solutions generated by the symmetry. By computing the boundary theory retarded Green's function we show the existence of a gapless mode with a diffusive dispersion relation. The diffusive character of the mode is compatible with the absence of a conserved charge from the field theory point of view. We give an analytic expression for the corresponding diffusion constant in terms of thermodynamic data and a new transport coefficient σ b which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap δω g as a simple function of σ b and of data of the thermal state. arXiv:1905.00398v2 [hep-th] 14 May 20191 Global symmetries are expected to be broken in a quantum theory of gravity [8,9] Nevertheless, they are perfectly well-behaved in the classical low-energy limit.2 Among other results, the authors of [10] considered the hydrodynamic limit of Green's functions in the case of gauged symmetry breaking in the bulk up to linear order in the wavenumber giving a holographic calculation of the speed of sound.

We consider thermal phases of holographic lattices at finite chemical potential in which a continuous internal bulk symmetry can be spontaneously broken. In the normal phase, translational symmetry is explicitly broken by the lattice and the only conserved quantities are related to time translations and the electric charge. The long wavelength excitations of the corresponding charge densities are described by incoherent hydrodynamics yielding two perturbative modes which are diffusive. In the broken phase an additional hydrodynamic degree of freedom couples to the local chemical potential and temperature and we write an effective theory describing the coupled system at leading order in a derivative expansion.

We investigate the convergence of relativistic hydrodynamics in charged fluids, within the framework of holography. On the one hand, we consider the analyticity properties of the dispersion relations of the hydrodynamic modes on the complex frequency and momentum plane and on the other hand, we perform a perturbative expansion of the dispersion relations in small momenta to a very high order. We see that the locations of the branch points extracted using the first approach are in good quantitative agreement with the radius of convergence extracted perturbatively. We see that for different values of the charge, different types of pole collisions set the radius of convergence. The latter turns out to be finite in the neutral case for all hydrodynamic modes, while it goes to zero at extremality for the shear and sound modes. Furthermore, we also establish the phenomenon of pole-skipping for the Reissner-Nordström black hole, and we find that the value of the momentum for which this phenomenon occurs need not be within the radius of convergence of hydrodynamics.