## Publications

168 results found

Ferrero P, Gauntlett JP, Ipina JMP,
et al., 2021, Accelerating black holes and spinning spindles, *Physical Review D: Particles, Fields, Gravitation and Cosmology*, Vol: 104, Pages: 1-37, ISSN: 1550-2368

We study solutions in the Plebański–Demiański family which describe an accelerating, rotating, and dyonically charged black hole in AdS4. These are solutions of D=4 Einstein-Maxwell theory with a negative cosmological constant and hence minimal D=4 gauged supergravity. It is well known that when the acceleration is nonvanishing the D=4 black hole metrics have conical singularities. By uplifting the solutions to D=11 supergravity using a regular Sasaki-Einstein seven-manifold, SE7, we show how the free parameters can be chosen to eliminate the conical singularities. Topologically, the D=11 solutions incorporate an SE7 fibration over a two-dimensional weighted projective space, WCP1[n−,n+], also known as a spindle, which is labeled by two integers that determine the conical singularities of the D=4 metrics. We also discuss the supersymmetric and extremal limit and show that the near horizon limit gives rise to a new family of regular supersymmetric AdS2×Y9 solutions of D=11 supergravity, which generalize a known family by the addition of a rotation parameter. We calculate the entropy of these black holes and argue that it should be possible to derive this from certain N=2, d=3 quiver gauge theories compactified on a spinning spindle with the appropriate magnetic flux.

Arav I, Gauntlett JP, Roberts MM,
et al., 2021, Marginal deformations and RG flows for type IIB S-folds, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-41, ISSN: 1029-8479

We construct a continuous one parameter family of AdS4 × S1 × S5 S-fold solutions of type IIB string theory which have nontrivial SL(2, ℤ) monodromy in the S1 direction. The solutions span a subset of a conformal manifold that contains the known N = 4 S-fold SCFT in d = 3, and generically preserve N = 2 supersymmetry. We also construct RG flows across dimensions, from AdS5 × S5, dual to N = 4, d = 4 SYM compactified with a twisted spatial circle, to various AdS4 ×S1 ×S5 S-fold solutions, dual to d = 3 SCFTs. We construct additional flows between the AdS5 dual of the Leigh-Strassler SCFT and an N = 2 S-fold as well as RG flows between various S-folds.

Arav I, Cheung KCM, Gauntlett JP,
et al., 2021, A new family of AdS4 S-folds in type IIB string theory, *The Journal of High Energy Physics*, Vol: 2021, Pages: 1-49, ISSN: 1029-8479

We construct infinite new classes of AdS4 × S1 × S5 solutions of type IIB string theory which have non-trivial SL(2, ℤ) monodromy along the S1 direction. The solutions are supersymmetric and holographically dual, generically, to N = 1 SCFTs in d = 3. The solutions are first constructed as AdS4 × ℝ solutions in D = 5 SO(6) gauged supergravity and then uplifted to D = 10. Unlike the known AdS4 × ℝ S-fold solutions, there is no continuous symmetry associated with the ℝ direction. The solutions all arise as limiting cases of Janus solutions of d = 4, N = 4 SYM theory which are supported both by a different value of the coupling constant on either side of the interface, as well as by fermion and boson mass deformations. As special cases, the construction recovers three known S-fold constructions, preserving N = 1, 2 and 4 supersymmetry, as well as a recently constructed N = 1 AdS4 × S1 × S5 solution (not S-folded). We also present some novel “one-sided Janus” solutions that are non-singular.

Ferrero P, Gauntlett JP, Ipiña JMP,
et al., 2021, D3-branes wrapped on a spindle, *Physical Review Letters*, Vol: 126, ISSN: 0031-9007

We construct supersymmetric AdS_{3}×Σ solutions of minimal gauged supergravity in D=5, where Σ is a two-dimensional orbifold known as a spindle. Remarkably, these uplift on S^{5}, or more generally on any regular Sasaki-Einstein manifold, to smooth solutions of type IIB supergravity. The solutions are dual to d=2, N=(0,2) SCFTs and we show that the central charge for the gravity solution agrees with a field theory calculation associated with D3-branes wrapped on Σ.

Arav I, Cheung KCM, Gauntlett JP, et al., 2020, Spatially modulated and supersymmetric mass deformations of N=4 SYM, Publisher: arXiv

We study mass deformations of $\mathcal{N}=4$, $d=4$ SYM theory that arespatially modulated in one spatial dimension and preserve some residualsupersymmetry. We focus on generalisations of $\mathcal{N}=1^*$ theories andshow that it is also possible, for suitably chosen supersymmetric masses, topreserve $d=3$ conformal symmetry associated with a co-dimension one interface.Holographic solutions can be constructed using $D=5$ theories of gravity thatarise from consistent truncations of $SO(6)$ gauged supergravity and hence typeIIB supergravity. For the mass deformations that preserve $d=3$ superconformalsymmetry we construct a rich set of Janus solutions of $\mathcal{N}=4$ SYMtheory which have the same coupling constant on either side of the interface.Limiting classes of these solutions give rise to RG interface solutions with$\mathcal{N}=4$ SYM on one side of the interface and the Leigh-Strassler (LS)SCFT on the other, and also to a Janus solution for the LS theory. Anotherlimiting solution is a new supersymmetric $AdS_4\times S^1\times S^5$ solutionof type IIB supergravity.

Arav I, Cheung KCM, Gauntlett JP, et al., 2020, Superconformal RG interfaces in holography, Publisher: arXiv

We construct gravitational solutions that holographically describe twodifferent $d=4$ SCFTs joined together at a co-dimension one, planar RGinterface and preserving $d=3$ superconformal symmetry. The RG interface joins$\mathcal{N}=4$ SYM theory on one side with the $\mathcal{N}=1$ Leigh-StrasslerSCFT on the other. We construct a family of such solutions, which in generalare associated with spatially dependent mass deformations on the$\mathcal{N}=4$ SYM side, but there is a particular solution for which thesedeformations vanish. We also construct a Janus solution with theLeigh-Strassler SCFT on either side of the interface. Gravitational solutionsassociated with superconformal interfaces involving ABJM theory and two $d=3$$\mathcal{N}=1$ SCFTs with $G_2$ symmetry are also discussed and shown to havesimilar properties, but they also exhibit some new features.

Donos A, Gauntlett JP, Pantelidou C, 2020, Holographic Abrikosov lattices, *The Journal of High Energy Physics*, Vol: 2020, Pages: 1-26, ISSN: 1029-8479

We study black hole solutions of D = 4 Einstein-Maxwell theory coupled to a charged scalar field that are holographically dual to a d = 3 conformal field theory with a non-vanishing chemical potential and constant magnetic field. We numerically construct black hole solutions that are dual to a superfluid phase with a periodic lattice of vortices. For the specific model we investigate, we find that the thermodynamically preferred con- figuration is given by a triangular lattice and moreover the vortices are associated with the lowest Landau level. We also construct black holes describing a lattice of vortices associated with the next to lowest Landau level and while these are not thermodynamically preferred they exhibit some interesting features that could be realised for other holographic models.

Gauntlett JP, Martelli D, Sparks J, 2019, Fibred GK geometry and supersymmetric AdS solutions, Publisher: arXiv

We continue our study of a general class of N=2 supersymmetric AdS3×Y7 and AdS2×Y9 solutions of type IIB and D=11 supergravity, respectively. The geometry of the internal spaces is part of a general family of "GK geometries", Y2n+1, n≥3, and here we study examples in which Y2n+1 fibres over a Kähler base manifold B2k, with toric fibres. We show that the flux quantization conditions, and an action function that determines the supersymmetric R-symmetry Killing vector of a geometry, may all be written in terms of the "master volume" of the fibre, together with certain global data associated with the Kähler base. In particular, this allows one to compute the central charge and entropy of the holographically dual (0,2) SCFT and dual superconformal quantum mechanics, respectively, without knowing the explicit form of the Y7 or Y9 geometry. We illustrate with a number of examples, finding agreement with explicit supergravity solutions in cases where these are known, and we also obtain new results. In addition we present, en passant, new formulae for calculating the volumes of Sasaki-Einstein manifolds.

Cheung KCM, Gauntlett JP, Rosen C, 2019, Consistent KK truncations for M5-branes wrapped on Riemann surfaces, *Classical and Quantum Gravity*, Vol: 36, ISSN: 0264-9381

We construct a consistent Kaluza–Klein reduction of D = 11 supergravityon Σ2 × S4, where Σ2 = S2, R2 or H2, or a quotient thereof, at the levelof the bosonic fields. The result is a gauged N = 4, D = 5 supergravitytheory coupled to three vector multiplets, with the gauging lying in anSO(2) × SE(3) ⊂ SO(5, 3) subgroup of the SO(1, 1) × SO(5, 3) globalsymmetry group of the ungauged theory. For Σ2 = H2, the D = 5 theoryhas a maximally supersymmetric AdS5 vacuum which uplifts to the knownsolution of D = 11 supergravity corresponding to M5-branes wrapping aRiemann surface with genus greater than one and dual to an N = 2 SCFTin d = 4. For Σ2 = S2, we find two AdS5 solutions, one of which is new, andboth of which are unstable. There is an additional subtruncation to an N = 2gauged supergravity coupled to two vector multiplets, with very special realmanifold SO(1, 1) × SO(1, 1), and a single hypermultiplet, with quaternionicKähler manifold SU(2, 1)/S[U(2) × U(1)] and gauging associated with anSO(2) × R ⊂ SU(2, 1) subgroup.

Gauntlett JP, Martelli D, Sparks J, 2019, Toric geometry and the dual of I-extremization, *The Journal of High Energy Physics*, Vol: 140, ISSN: 1029-8479

We consider d=3, N=2 gauge theories arising on membranes sitting at the apex of an arbitrary toric Calabi-Yau 4-fold cone singularity that are then further compactified on a Riemann surface, Σg, with a topological twist that preserves two supersymmetries. If the theories flow to a superconformal quantum mechanics in the infrared, then they have a D=11 supergravity dual of the form AdS2×Y9, with electric four-form flux and where Y9 is topologically a fibration of a Sasakian Y7 over Σg. These D=11 solutions are also expected to arise as the near horizon limit of magnetically charged black holes in AdS4×Y7, with a Sasaki-Einstein metric on Y7. We show that an off-shell entropy function for the dual AdS2 solutions may be computed using the toric data and Kähler class parameters of the Calabi-Yau 4-fold, that are encoded in a master volume, as well as a set of integers that determine the fibration of Y7 over Σg and a Kähler class parameter for Σg. We also discuss the class of supersymmetric AdS3×Y7 solutions of type IIB supergravity with five-form flux only in the case that Y7 is toric, and show how the off-shell central charge of the dual field theory can be obtained from the toric data. We illustrate with several examples, finding agreement both with explicit supergravity solutions as well as with some known field theory results concerning I-extremization.

Arav I, Gauntlett JP, Roberts M,
et al., 2019, Spatially modulated and supersymmetric deformations of ABJM theory, *Journal of High Energy Physics*, Vol: 2019, ISSN: 1029-8479

We construct supersymmetric solutions of $D=11$ supergravity, preserving 1/4of the supersymmetry, that are holographically dual to ABJM theory which hasbeen deformed by spatially varying mass terms depending on one of the twospatial directions. We show that the BPS equations reduce to the Helmholtzequation on the complex plane leading to rich classes of new solutions. Inparticular, the construction gives rise to infinite classes of supersymmetricboomerang RG flows, as well as generalising a known Janus solution.

Couzens C, Gauntlett JP, Martelli D,
et al., 2019, A geometric dual of c-extremization, *Journal of High Energy Physics*, Vol: 2019, Pages: 1-55, ISSN: 1029-8479

We consider supersymmetric AdS3 × Y7 and AdS2 × Y9 solutions of type IIBand D = 11 supergravity, respectively, that are holographically dual to SCFTs with (0, 2)supersymmetry in two dimensions and N = 2 supersymmetry in one dimension. Thegeometry of Y2n+1, which can be defined for n ≥ 3, shares many similarities with SasakiEinstein geometry, including the existence of a canonical R-symmetry Killing vector, butthere are also some crucial differences. We show that the R-symmetry Killing vector maybe determined by extremizing a function that depends only on certain global, topologicaldata. In particular, assuming it exists, for n = 3 one can compute the central charge ofan AdS3 × Y7 solution without knowing its explicit form. We interpret this as a geometricdual of c-extremization in (0, 2) SCFTs. For the case of AdS2 × Y9 solutions we show thatthe extremal problem can be used to obtain properties of the dual quantum mechanics,including obtaining the entropy of a class of supersymmetric black holes in AdS4. We alsostudy many specific examples of the type AdS3×T2×Y5, including a new family of explicitsupergravity solutions. In addition we discuss the possibility that the (0, 2) SCFTs dualto these solutions can arise from the compactification on T2 of certain d = 4 quiver gaugetheories associated with five-dimensional Sasaki-Einstein metrics and, surprisingly, cometo a negative conclusion.

Gauntlett JP, Martelli D, Sparks J, 2019, Toric geometry and the dual of c-extremization, *Journal of High Energy Physics*, Vol: 2019, ISSN: 1029-8479

We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface Σg, with an arbitrary partial topological twist for the global U(1) symmetries. This constitutes a rich, infinite class of two-dimensional (0, 2) theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and R-charges of BPS baryonic operators of the dual AdS3 solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the Yp,q and Xp,q 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using c-extremization, for arbitrary twist over Σg. We furthermore conjecture that the trial central charge Open image in new window , which we define in gravity, matches the field theory trial c-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions.

Gauntlett JP, Rosen C, 2018, Susy Q and spatially modulated deformations of ABJM theory, *Journal of High Energy Physics*, Vol: 2018, ISSN: 1029-8479

Within a holographic framework we construct supersymmetric Q-lattice (‘Susy Q’) solutions that describe RG flows driven by supersymmetric and spatially modulated deformations of the dual CFTs. We focus on a specific D = 4 supergravity model which arises as a consistent KK truncation of D = 11 supergravity on the seven sphere that preserves SO(4) × SO(4) symmetry. The Susy Q solutions are dual to boomerang RG flows, flowing from ABJM theory in the UV, deformed by spatially modulated mass terms depending on one of the spatial directions, back to the ABJM vacuum in the far IR. For large enough deformations the boomerang flows approach the well known Poincaré invariant RG dielectric flow. The spatially averaged energy density vanishes for the Susy Q solutions.

Donos A, Gauntlett JP, Griffin T,
et al., 2018, Incoherent transport for phases that spontaneously break translations, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2018, ISSN: 1029-8479

We consider phases of matter at finite charge density which spontaneously break spatial translations. Without taking a hydrodynamic limit we identify a boost invariant incoherent current operator. We also derive expressions for the small frequency behaviour of the thermoelectric conductivities generalising those that have been derived in a translationally invariant context. Within holographic constructions we show that the DC conductivity for the incoherent current can be obtained from a solution to a Stokes flow for an auxiliary fluid on the black hole horizon combined with specific thermodynamic quantities associated with the equilibrium black hole solutions.

Donos A, Gauntlett JP, Rosen C,
et al., 2018, Boomerang RG flows with intermediate conformal invariance, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2018, ISSN: 1029-8479

For a class of D = 5 holographic models we construct boomerang RG flow solutions that start in the UV at an AdS5 vacuum and end up at the same vacuum in the IR. The RG flows are driven by deformations by relevant operators that explicitly break translation invariance. For specific models, such that they admit another AdS5 solution, AdS 5 c , we show that for large enough deformations the RG flows approach an intermediate scaling regime with approximate conformal invariance governed by AdS 5 c . For these flows we calculate the holographic entanglement entropy and the entropic c-function for the RG flows. The latter is not monotonic, but it does encapsulate the degrees of freedom in each scaling region. For a different set of models, we find boomerang RG flows with intermediate scaling governed by an AdS2 × ℝ3 solution which breaks translation invariance. Furthermore, for large enough deformations these models have interesting and novel thermal insulating ground states for which the entropy vanishes as the temperature goes to zero, but not as a power-law. Remarkably, the thermal diffusivity and the butterfly velocity for these new insulating ground states are related via D = Ev B 2 /(2πT), with E(T) → 0.5 as T → 0.

Donos A, Gauntlett JP, Ziogas V, 2018, Diffusion for holographic lattices, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

Donos A, Gauntlett JP, Ziogas V, 2017, Diffusion in inhomogeneous media, *Physical Review D - Particles, Fields, Gravitation and Cosmology*, Vol: 96, ISSN: 1550-2368

We consider the transport of conserved charges in spatially inhomogeneous quantum systems with a discrete lattice symmetry. We analyze the retarded two-point functions involving the charges and the associated currents at long wavelengths, compared to the scale of the lattice, and, when the dc conductivities are finite, extract the hydrodynamic modes associated with diffusion of the charges. We show that the dispersion relations of these modes are related to the eigenvalues of a specific matrix constructed from the dc conductivities and certain thermodynamic susceptibilities, thus obtaining generalized Einstein relations. We illustrate these general results in the specific context of relativistic hydrodynamics where translation invariance is broken using spatially inhomogeneous and periodic deformations of the stress tensor and the conserved U(1) currents. Equivalently, this corresponds to considering hydrodynamics on a curved manifold, with a spatially periodic metric and chemical potential, and we obtain the dispersion relations for the heat and charge diffusive modes.

Donos A, Gauntlett JP, Rosen C,
et al., 2017, Boomerang RG flows in M-theory with intermediate scaling, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2017, ISSN: 1029-8479

We construct novel RG flows of D=11 supergravity that asymptotically approach AdS4 × S7 in the UV with deformations that break spatial translations in the dual field theory. In the IR the solutions return to exactly the same AdS4 × S7 vacuum, with a renormalisation of relative length scales, and hence we refer to the flows as ‘boomerang RG flows’. For sufficiently large deformations, on the way to the IR the solutions also approach two distinct intermediate scaling regimes, each with hyperscaling violation. The first regime is Lorentz invariant with dynamical exponent z = 1 while the second has z = 5/2. Neither ofthe two intermediatescaling regimesare associatedwith exact hyperscaling violation solutions of D = 11 supergravity. The RG flow solutions are constructed using the four dimensional N = 2 STU gauged supergravity theory with vanishing gauge fields, but non-vanishing scalar and pseudoscalar fields. In the ABJM dual field theory the flows are driven by spatially modulated deformation parameters for scalar and fermion bilinear operators.

Donos A, Gauntlett JP, Griffin T,
et al., 2017, Holographic DC conductivity and Onsager relations, *Journal of High Energy Physics*, Vol: 2017, ISSN: 1029-8479

Within holography the DC conductivity can be obtained by solving a system of Stokes equations for an auxiliary fluid living on the black hole horizon. We show that these equations can be derived from a novel variational principle involving a functional that depends on the fluid variables of interest as well as the time reversed quantities. This leads to simple derivation of the Onsager relations for the conductivity. We also obtain the relevant Stokes equations for bulk theories of gravity in four dimensions including a ϑF ∧ F term in the Lagrangian, where ϑ is a function of dynamical scalar fields. We discuss various realisations of the anomalous Hall conductivity that this term induces and also solve the Stokes equations for holographic lattices which break translations in one spatial dimension.

Donos A, Gauntlett JP, Griffin T,
et al., 2017, DC conductivity and higher derivative gravity, *Classical and Quantum Gravity*, Vol: 34, ISSN: 0264-9381

For Gauss–Bonnet gravity and in the context of holography we show how the thermal DC conductivity can be obtained by solving a generalised system of Stokes equations for an auxiliary fluid on a curved black hole horizon. For more general higher derivative theories of gravity coupled to gauge-fields, we also analyse the linearised thermal and electric currents that are produced by DC thermal and electric sources. We show how suitably defined DC transport current fluxes of the dual field theory are given by current fluxes defined at the black horizon.

Banks E, Donos A, Gauntlett JP,
et al., 2017, Thermal backflow in CFTs, *PHYSICAL REVIEW D*, Vol: 95, ISSN: 2470-0010

Banks E, Donos A, Gauntlett JP,
et al., 2017, Thermal backflow in CFTs, *Physical Review D*, Vol: 95, ISSN: 1550-7998

We study the thermal transport properties of general conformal field theories (CFTs) on curved spacetimes in the leading order viscous hydrodynamic limit. At the level of linear response, we show that the thermal transport is governed by a system of forced linearized Navier-Stokes equations on a curved space. Our setup includes CFTs in flat spacetime that have been deformed by spatially dependent and periodic local temperature variations or strains that have been applied to the CFT, and hence is relevant to CFTs arising in condensed matter systems at zero charge density. We provide specific examples of deformations which lead to thermal backflow driven by a dc source: that is, the thermal currents locally flow in the opposite direction to the applied dc thermal source. We also consider thermal transport for relativistic quantum field theories that are not conformally invariant.

Banks E, Donos A, Gauntlett JP,
et al., 2017, Holographic thermal DC response in the hydrodynamic limit, *Classical and Quantum Gravity*, Vol: 34, ISSN: 1361-6382

We consider black hole solutions of Einstein gravity that describe deformations of CFTs at finite temperature in which spatial translations have been broken explicitly. We focus on deformations that are periodic in the non-compact spatial directions, which effectively corresponds to considering the CFT on a spatial torus with a non-trivial metric. We apply a DC thermal gradient and show that in a hydrodynamic limit the linearised, local thermal currents can be determined by solving linearised, forced Navier–Stokes equations for an incompressible fluid on the torus. We also show how sub-leading corrections to the thermal current can be calculated as well as showing how the full stress tensor response that is generated by the DC source can be obtained. We also compare our results with the fluid-gravity approach.

Donos A, Gauntlett JP, Sosa-Rodriguez O, 2016, Anisotropic plasmas from axion and dilaton deformations, *The Journal of High Energy Physics*, Vol: 2016, ISSN: 1029-8479

We construct black hole solutions of type IIB supergravity that are holographically dual to anisotropic plasmas arising from deformations of an infinite class of four-dimensional CFTs. The CFTs are dual to AdS5 × X5, where X5 is an Einstein manifold, and the deformations involve the type IIB axion and dilaton, with non-trivial periodic dependence on one of the spatial directions of the CFT. At low temperatures the solutions approach smooth domain wall solutions with the same AdS5 × X5 solution appearing in the far IR. For sufficiently large deformations an intermediate scaling regime appears which is governed by a Lifshitz-like scaling solution. We calculate the DC thermal conductivity and some components of the shear viscosity tensor.

Gauntlett J, 2016, Thomas Kibble (1932-2016) Theoretical physicist and Higgs-boson pioneer. OBITUARY, *Nature*, Vol: 534, Pages: 622-622, ISSN: 0028-0836

Donos A, Gauntlett JP, 2016, Minimally packed phases in holography, *Journal of High Energy Physics*, Vol: 2016, ISSN: 1126-6708

We numerically construct asymptotically AdS black brane solutions of $D=4$Einstein-Maxwell theory coupled to a pseudoscalar. The solutions areholographically dual to $d=3$ CFTs at finite chemical potential and in aconstant magnetic field, which spontaneously break translation invarianceleading to the spontaneous formation of abelian and momentum magnetisationcurrents flowing around the plaquettes of a periodic Bravais lattice. Weanalyse the three-dimensional moduli space of lattice solutions, which aregenerically oblique, and show, for a specific value of the magnetic field, thatthe free energy is minimised by the triangular lattice, associated with minimalpacking of circles in the plane. We show that the average stress tensor for thethermodynamically preferred phase is that of a perfect fluid and that thisresult applies more generally to spontaneously generated periodic phases. Thetriangular structure persists at low temperatures indicating the existence ofnovel crystalline ground states.

Donos A, Gauntlett JP, Griffin T,
et al., 2016, DC Conductivity of Magnetised Holographic Matter, *Journal of High Energy Physics*, Vol: 2016, ISSN: 1126-6708

We consider general black hole solutions of Einstein-Maxwell-scalar theorythat are holographically dual to conformal field theories at finite chargedensity with non-vanishing magnetic fields and local magnetisation currents,which generically break translation invariance explicitly. We show that thethermoelectric DC conductivity of the field theory can be obtained by solving asystem of generalised Stokes equations on the black hole horizon. For variousexamples, including Q-lattices and one-dimensional lattices, we solve theStokes equations explicitly and obtain expressions for the DC conductivity interms of the solution at the black hole horizon.

Donos A, Gauntlett JP, 2015, Navier-Stokes equations on black hole horizons and DC thermoelectric conductivity, *Physical Review D*, Vol: 92, ISSN: 1550-7998

Within the context of the AdS/CFT correspondence, we show that the DC thermoelectric conductivity can be obtained by solving the linearized, time-independent, and forced Navier-Stokes equations on the black hole horizon for an incompressible and charged fluid.

Banks E, Donos A, Gauntlett JP, 2015, Thermoelectric DC conductivities and Stokes flows on black hole horizons, *Journal of High Energy Physics*, Vol: 2015, ISSN: 1126-6708

We consider a general class of electrically charged black holes of EinsteinMaxwell-scalartheory that are holographically dual to conformal field theories at finitecharge density which break translation invariance explicitly. We examine the linearisedperturbations about the solutions that are associated with the thermoelectric DC conductivity.We show that there is a decoupled sector at the black hole horizon which must solvegeneralised Stokes equations for a charged fluid. By solving these equations we can obtainthe DC conductivity of the dual field theory. For Q-lattices and one-dimensional latticeswe solve the fluid equations to obtain closed form expressions for the DC conductivity interms of the solution at the black hole horizon. We also determine the leading order DCconductivity for lattices that can be expanded as a perturbative series about translationallyinvariant solutions.

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