Classical Fermi Fluid and Geometric Action for $c=1$

Abstract

We formulate the $c=1$ matrix model as a quantum fluid and discuss its classical limit in detail, emphasizing the $\hslash$ corrections. We view the fermi fluid profiles as elements of \winf-coadjoint orbit and write down a geometric action for the classical phase space. In the specific representation of fluid profiles as `strings' the action is written in a four-dimensional form in terms of gauge fields built out of the embedding of the `string' in the phase plane. We show that the collective field action can be derived from the above action provided one restricts to quadratic fluid profiles and ignores the dynamics of their `turning points'.

31 pages. (Revised version)

Cited by in corpus (38)

• The Library of Babel: On the origin of gravitational thermodynamics
• Fermions from Half-BPS Supergravity
• Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Nonlinear Bosonization of Fermi Surfaces: The Method of Coadjoint Orbits
• Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons
• Thermal Emission from Semi-classical Dynamical Systems
• Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries
• Folds, Bosonization and non-triviality of the classical limit of 2D string theory
• Quantum quench in matrix models: Dynamical phase transitions, Selective equilibration and the Generalized Gibbs Ensemble
• Electromagnetic interactions of higher dimensional quantum Hall droplets
• Quantum quench and thermalization of one-dimensional Fermi gas via phase space hydrodynamics
• Exact operator bosonization of finite number of fermions in one space dimension
• Bosonization of non-relativstic fermions in 2-dimensions and collective field theory
• Discrete State Moduli of String Theory from c=1 Matrix Model
• Emergent classical spacetime from microstates of an incipient black hole
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Quantum Quench in Non-relativistic Fermionic Field Theory: Harmonic traps and 2d String Theory
• Symmetries and tau function of higher dimensional dispersionless integrable hierarchies
• Degrees of freedom in two dimensional string theory
• Plasma balls/kinks as solitons of large $N$ confining gauge theories
• Thermofield dynamics and Gravity
• Limit shape phase transitions: a merger of arctic circles
• String Beta Function Equations From c=1 Matrix Model
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory
• Open String Descriptions of Space-like Singularities in Two Dimensional String Theory
• Finiteness of Entanglement Entropy in Collective Field Theory
• Phase Space Distribution of Riemann Zeros
• Quantum behaviour near a spacelike boundary in the c=1 matrix model
• The fermion density operator in the droplet bosonization picture
• Higher Spin Gravity in $Ad{S}_3$ and Folds on Fermi Surface
• Phase space holography with no strings attached
• Nonequilibrium dynamics of noninteracting fermions in a trap
• Entanglement Entropy and Phase Space Density: Lowest Landau Levels and 1/2 BPS states
• Exact operator Hamiltonians and interactions in the droplet bosonization method
• Bound on Lyapunov exponent in $c=1$ matrix model
• Quantum curves as quantum distributions
• Vacuum States in 2D Tachyon Effective Action