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01 / Research theme
Holography, hydrodynamics & horizon symmetries
How much of the dynamics of a strongly interacting quantum system can be learned from symmetry—and from a black-hole horizon?
The idea
What is the question?
At long distances, very different many-body systems can behave like fluids. Their microscopic details matter through a small set of quantities, such as viscosity and resistivity, while conservation laws organise the allowed dynamics. I study this universal description and the ways it changes when a quantum anomaly obstructs an ordinary conservation law.
A simple example is the decay of a long-wavelength disturbance. Diffusion smooths spatial variation, with shorter wavelengths relaxing faster. The interesting research problem is to derive the effective dynamics—including dissipation and fluctuations—from the underlying symmetries or from a gravitational description, rather than insert a damping law by hand.
Explore an idea
A little physics to play with.
Change the controls and watch what follows.
Interactive intuition · Fluid / gravity
A fluid at the boundary.
A membrane near the horizon.
Explore how a black-brane spacetime encodes fluid dynamics, then watch a transverse shear pattern relax. The two views connect the geometric picture to the physics of viscosity.
01 / The gravitational picture
Explore the layers.
Select a layer to see what it represents. Play the shear experiment below to animate the velocity arrows on both surfaces.
Boundary fluidStretched horizonEvent horizon
The fluid–gravity dictionary
A slowly varying boundary fluid is described by a corresponding, long-wavelength deformation of a black-brane geometry. The radial direction belongs to the gravity description; the boundary fluid does not physically fall through it.
02 / The viscous response
Shear, stress and relaxation.
Neighbouring strips flow in opposite directions. Viscosity transfers transverse momentum between them, smoothing the velocity pattern. The highlighted probe reads the local velocity and shear stress.
Reduced motion is enabled. Use the time slider to explore still frames.
Each drawing spans one wavelength: λ = 2π/k = length units. The drawing width rescales when k changes.
Remaining amplitude / A
Decay rate νk²
Velocity at the probe
Shear stress at the probe
vy = A cos(kx) e−νk²t
πxy = −η ∂xvy
Try this: double k at a fixed viscosity. The mode decays four times faster. Move the probe from a velocity peak to the point between opposite flows: the velocity becomes zero while the magnitude of the shear stress becomes largest. The plots show one wavelength, λ = 2π/k, with velocity and stress normalized separately.
Model and scope. The shear mode solves linearized, first-order hydrodynamics: ∂tvy = ν∂x²vy, with ν = η/(ε + p). Units are scaled so ε + p = 1 and A = 0.12. The wavelengths are understood to be long compared with microscopic scales. The layered spacetime is schematic, not a computed bulk solution or a literal displacement of the horizon. Matching arrow patterns on the boundary and membrane illustrate a correspondence, not an equality of their local velocities or a computed radial profile. Boundary and membrane stresses are not being identified point by point; away from the low-frequency limit their relation involves radial evolution.
Connection to my research. This gives the physical setting for studying horizon symmetries, gravitational boundary conditions and the effective actions of holographic fluids.
Holography supplies a complementary viewpoint: the thermal state of a quantum field theory can be described by a black hole in a higher-dimensional spacetime. In recent work, I derive actions for the fluid variables directly from gravity. The variables are relative coordinate transformations between the asymptotic boundary and the horizon, so a question about fluid dynamics becomes a question about which geometric transformations the horizon permits.
A second strand follows chiral plasmas with dynamical electromagnetic fields. Here magnetic-flux conservation is a one-form symmetry. Combining effective theory, holographic calculations and classical lattice simulations makes it possible to test which transport predictions survive beyond a weakly coupled description.
Horizon symmetries are especially useful because they distinguish physical observables from redundancies in the variables used to describe them. In JT and AdS₃ gravity, different acceptable horizon boundary conditions can lead to different actions and symmetry transformations while giving the same stress-tensor two-point functions. Understanding this freedom is also important when investigating proposed connections between hydrodynamics and quantum chaos.
The aim is to identify which features of transport and thermal dynamics are fixed by symmetry, which depend on microscopic information, and how horizon geometry encodes that distinction.
The toolkit
How I approach it.
Partially on-shell gravitational actions and horizon boundary conditions
Higher-form symmetries and anomalous magnetohydrodynamics
Kubo formulas, real-time lattice simulations and hydrodynamic loop corrections
Research contributions
What the work shows.
- Derived dissipative stress-tensor actions from AdS₄ gravity and exact-in-derivatives quadratic actions in JT/AdS₃ gravity.arXiv:2607.00866 →arXiv:2610.12262 →
- Related horizon-preserving diffeomorphisms to redundancies of hydrodynamic actions, clarifying the dependence on horizon boundary conditions.arXiv:2610.12262 →
- Computed and tested axial charge relaxation using the magnetic-flux formulation of the anomaly.arXiv:2205.03619 →arXiv:2212.09787 →arXiv:2309.14438 →
- Showed that one-loop hydrodynamic fluctuations do not generate a finite zero-field axial relaxation rate.arXiv:2403.16957 →
Where these results apply. The gravity calculations have stated amplitude and derivative regimes. The relationship to quantum chaos is a precise research question, not a claim that every horizon symmetry directly measures an out-of-time-order correlator.
Read further
Papers in this direction.
Horizon symmetries of exact hydrodynamic actions
Key results4 highlights
Connects gravitational horizon symmetries to explicit fluid actions in two solvable holographic settings.
- Derives hydrodynamic actions for small perturbations of JT and AdS₃ black holes, without truncating the derivative expansion.
- Shows that diffeomorphisms preserving the chosen horizon boundary conditions act as symmetries of the hydrodynamic fields.
- Writes compact diffeomorphism- and Weyl-covariant actions, and recovers the Schwarzian action in the source-free JT limit.
- Compares horizon boundary conditions: Dirichlet and alternative choices give different actions and redundancies while reproducing the same stress-tensor two-point functions.
Scope. Exact in derivatives within the small-amplitude expansion; this is not a full nonlinear action or a higher-dimensional proof of the proposed chaos mechanism.
Dissipative hydrodynamic actions and horizon symmetries in gravity
Key results4 highlights
Builds a gravitational prescription for the fluctuating, dissipative stress-tensor dynamics of a thermal quantum field theory.
- Constructs a Schwinger–Keldysh hydrodynamic action from metric perturbations of an AdS₄ black brane.
- Identifies the fluid variables as relative diffeomorphisms between the horizon and the two asymptotic boundaries of the gravitational contour.
- Computes the action to quadratic order in fluctuations and first order in derivatives, reproducing known hydrodynamic Green functions and fluctuation–dissipation relations.
- Classifies horizon-preserving transformations and tests the time-independent shifts directly on the resulting constitutive relations.
Scope. The calculation is perturbative in amplitudes and derivatives. Exponential horizon modes are identified, but proving that they are symmetries of the complete action requires all derivative orders.
Hydrodynamic fluctuations and topological susceptibility in chiral magnetohydrodynamics
Key results4 highlights
Tests whether thermal fluctuations destroy the slow axial charge at zero background magnetic field.
- Computes the retarded topological-density correlator at one loop in magnetohydrodynamic fluctuations around a state with zero magnetic field.
- Extracts its low-frequency behaviour and the associated fluctuation contribution to axial charge relaxation.
- Finds that this contribution vanishes in the zero-frequency limit, so no finite axial decay rate is generated at this order.
- Identifies nonanalytic low-frequency terms fixed by hydrodynamic data and explains the special role of magnetic-flux conservation in the Abelian theory.
Scope. The vanishing relaxation-rate result is established at one loop in hydrodynamics, not to all fluctuation orders or for non-Abelian plasmas.
Higher-form symmetry and chiral transport in real-time Abelian lattice gauge theory
Key results4 highlights
Checks the higher-form-symmetry description of a plasma against real-time lattice dynamics.
- Measures transport coefficients in classical finite-temperature lattice simulations of electrodynamics coupled to charged matter.
- Shows that resistivity defined through the electric-field Kubo formula predicts magnetic diffusion and axial charge relaxation.
- Explains why the usual low-frequency conductivity Kubo formula vanishes when electromagnetic fields are dynamical and fully thermalised.
- Resolves a previous mismatch between simulated chiral relaxation rates and hydrodynamic estimates by using the appropriate transport coefficients.
Scope. The evidence comes from classical lattice simulations of the specified Abelian plasma; identifying resistivity with inverse conductivity requires additional scale separation.
Towards an effective action for chiral magnetohydrodynamics
Key results4 highlights
Develops symmetry-based effective descriptions of a plasma with an axial anomaly and dynamical electromagnetism.
- Recasts the Adler–Bell–Jackiw anomaly in terms of the conserved two-form current associated with magnetic flux.
- Builds equilibrium generating-functional and dissipative-action descriptions that reproduce aspects of the chiral separation and chiral magnetic effects.
- Derives a weak-field axial-relaxation expression in terms of resistivity and susceptibility, rather than assuming a conventional conductivity description.
- Discusses non-invertible axial defect operators within the same effective-theory framework.
Scope. The paper presents progress towards a general action. It does not claim a complete universal equilibrium functional or an all-orders proof of the relaxation formula.
Higher-form symmetries, anomalous magnetohydrodynamics, and holography
Key results4 highlights
Constructs a holographic laboratory for axial charge relaxation in a magnetised chiral plasma.
- Builds a holographic model whose symmetry structure combines magnetic-flux conservation with an anomalous axial current.
- Computes the axial susceptibility and relaxation rate as functions of temperature and background magnetic field.
- Derives the weak-field quadratic magnetic-field dependence analytically and matches its coefficient to magnetohydrodynamic expectations.
- Finds deviations from the elementary weak-field prediction at stronger magnetic fields and compares the results with lattice studies.
Scope. The strong-field results belong to the constructed holographic model; matching symmetry structure does not make it a microscopic dual of weakly coupled QED.
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