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Fluid/p-form duality
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Fluid/p-form duality
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In this study, we demonstrate that an inviscid fluid in a near-equilibrium state, when viewed in the Lagrangian picture in d+1 spacetime dimensions, can be reformulated as a (d-1)-form gauge theory. We construct a fluid/p-form dictionary and show that volume-preserving diffeomorphisms on the fluid side manifest as a U(1) gauge symmetry on the {(p+1)-form} gauge theory side. {Intriguingly, Kelvin's circulation theorem and the mass continuity equation respectively appear as the Gauss law and the Bianchi identity on the gauge theory side.} Furthermore, we show that at the level of the sources, the vortices in the fluid side correspond to the p-branes in the gauge theory side. We also consider fluid mechanics in the presence of boundaries and examine the boundary symmetries and corresponding charges from both the fluid and gauge theory perspectives.
Forward citations
Cited by 2 Pith papers
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The Schrodinger Equation as a Gauge Theory
The Schrödinger equation is locally equivalent to a gauge theory with one-form fields in 2+1D and two-form fields in 3+1D, with BF and Chern-Simons terms organizing electromagnetic couplings, anyons, Berry phases, and...
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The Schrodinger Equation as a Gauge Theory
Schrödinger equation is locally equivalent to a non-relativistic gauge theory via one-form or two-form gauge fields on the probability current, with global topology from phase winding quantization.
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