Gravitational duality, topologically massive gravity and holographic fluids

TL;DR

The work investigates gravitational duality and Weyl/Cotton self-duality in holography, deriving a boundary condition that links the energy–momentum tensor to the Cotton tensor via $8\,\pi G_N k^2 T^{\mu\nu} \pm C^{\mu\nu}=0$, and showing how this can lead to exact bulk Einstein spaces. By translating bulk self-duality into boundary data through Fefferman–Graham expansions, the authors demonstrate integrability and resummation into exact solutions in Lorentzian settings, with implications for holographic fluids. In particular, they construct perfect-equilibrium holographic fluids on Papapetrou–Randers backgrounds and classify boundary geometries with perfect Cotton tensors, whose bulk duals are AdS black holes of Plebański–Demiański type D. The results imply that certain backgrounds enforce vanishing of infinite families of transport coefficients, revealing deep connections between boundary gravitational dynamics (including topological mass terms) and fluid transport in the holographic dual. This framework paves the way for exploring boundary graviton dynamics and higher-dimensional generalizations within holography.

Abstract

Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the boundary energy-momentum tensor and the boundary Cotton tensor. This relationship, which can be viewed as resulting from a topological mass term for gravity boundary dynamics, survives under the Lorentzian signature and provides a tool for generating exact bulk Einstein spaces carrying, among others, nut charge. In turn, the holographic analysis exhibits perfect-fluid-like equilibrium states and the presence of non-trivial vorticity allows to show that infinite number of transport coefficients vanish.