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Non-relativistic Fermions, Coadjoint Orbits of \winf\ and String Field Theory at $c=1$
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abstract
We apply the method of coadjoint orbits of \winf-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space distribution of the fermi fluid. The action has an infinite series expansion in the string coupling, which to leading order reduces to the previously discussed geometric action for the classical fermi fluid based on the group $w_\infty$ of area-preserving diffeomorphisms. We briefly discuss the strong coupling limit of the string theory which, unlike the weak coupling regime, does not seem to admit of a two dimensional space-time picture. Our methods are equally applicable to interacting fermions in one dimension.
Forward citations
Cited by 3 Pith papers
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Effective Field Theory of Noncritical M-theory from Bosonization
Coadjoint-orbit bosonization of the Hořava-Keeler noncritical M-theory Fermi liquid yields a continuous family of interacting 1+1d chiral bosons whose density correlators match the exact Fermi liquid semiclassically.
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Higher-order chiral scalar from boundary reduction of 3d higher-spin gravity
Boundary reduction of 3d higher-spin Chern-Simons gravity yields covariant and gauge-fixed higher-derivative chiral-scalar actions for arbitrary spin s, with a factorized kinetic operator and special zero-mode backgrounds.
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Bosonization, BTZ Black Hole Microstates, and Logarithmic Correction to Entropy
BTZ black hole microstates under collective-field boundary conditions are labeled by Young diagrams, and the logarithmic correction to their entropy is -1/2, one-loop exact and identical for two boundary Hamiltonians.
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