Higher-form (Quasi)Hydrodynamics from Holography: Deformations and Dualities

TL;DR

This work develops a comprehensive holographic framework for systems with exact and approximate higher-form symmetries, modelling them with Maxwell-type bulk p-forms in AlAdS spacetimes and implementing boundary double-trace deformations. A unified dictionary connects quantisation (electric vs magnetic), bulk form rank and deformation scale, enabling analysis of both massless (exact) and massive (weakly broken) cases. Finite-temperature holography on isotropic black branes yields a rich spectrum of hydrodynamic, quasihydrodynamic, and emergent photon modes, with dualities mapping electric to magnetic descriptions and relating massive to massless regimes. The results extend bottom-up holography to deformed higher-form systems, uncover self-duality structures, and pave the way for generalized self-duality constraints and new deformed holographic duals with potential applications to generalized EFTs like Hydro+ and quasihydrodynamics.

Abstract

We study the low-energy dynamics of systems with exact and approximate higher-form symmetries using gauge/gravity duality. These symmetries are realised holographically via Maxwell-type theories for massless and massive $p$-forms in AlAdS spacetimes. Double-trace deformations of the boundary theory are considered. While massless theories describe systems with conserved higher-form current, the massive case provides a controlled linearised framework for explicit symmetry breaking induced by defects and charged operators. We perform holographic renormalisation and establish a unified holographic dictionary across a broad theory space, parametrised by spacetime dimension, form rank, quantisation scheme and deformation scale. We compute thermal correlation functions in isotropic black brane backgrounds to characterise the hydrodynamic and quasihydrodynamic regimes of the dual boundary theories. Our analysis reveals a rich structure of relaxation dynamics, emergent photons and duality relations -- including the conventional electric-magnetic Hodge duality and its massive counterpart. These results extend bottom-up holography to include weakly broken higher-form symmetries and open avenues for exploring generalised self-duality constraints and new classes of deformed holographic duals.

Figures (3)

• Figure 1: 1-form symmetry with defects: on the left, time is indicated as running vertically; in the middle, two infinitely extended strings and their worldsheets are shown --- the 1-form symmetry is reflected in the fact that the number of intersections between the worldsheets and a codimension-2 hypersurface is topological; on the right, the symmetry is broken by a 0-dimensional defect consisting of a junction from which two strings emanate (or into which they merge).
• Figure 2: Illustration of a double-trace deformation's effect on thermal spectra (at low-energies) of holographic duals to $p$-forms in the electric quantisation: $m^2 = 0$ (top) and $|m^2| \ll 1$ (bottom).
• Figure 3: A schematic depiction of the modes that populate the spectrum of each theory at low energies. On the left, for $d \geq 2$, we have spectra of duals to the massless theories with electric (magnetic) quantisation on top (bottom). Likewise, for $0 \leq n \leq d - 2$ and $d \geq 3$ the right-hand side refers to the massive case where electric (magnetic) quantisation is at the bottom (top). While undeformed theories sit at the ${\bar{\lambda}}$ and $\lambda$ axes, theories with infinitely large deformation sit at the opposite end of the coloured diagonal lines. We use a solid or a hollow dot to indicate respectively if a mode is or is not part of the spectrum in such cases. Additionally, we use a dashed line to signal that a gapped mode is entering the low-energy spectrum and a dashed circle around theories where the point at which a non-analytic point of the dispersion relation is accessible. The modes displayed are carried by the boxed operators.