Matrix model for a quantum Hall droplet with manifest particle-hole symmetry
Abstract
We find that a gauged matrix model of rectangular fermionic matrices (a matrix version of the fermion harmonic oscillator) realizes a quantum hall droplet with manifest particle-hole symmetry. The droplet consists of free fermions on the topology of a sphere. It is also possible to deform the Hamiltonian by double trace operators, and we argue that this device can produce two body potentials which might lead the system to realize a fractional quantum hall state on the sphere. We also argue that a single gauged fermionic quantum mechanics of Hermitian matrices realizes a droplet with an edge that has c=1/2 CFT on it.
- Publication:
-
Physical Review D
- Pub Date:
- April 2005
- DOI:
- 10.1103/PhysRevD.71.085001
- arXiv:
- arXiv:hep-th/0409115
- Bibcode:
- 2005PhRvD..71h5001B
- Keywords:
-
- 11.10.Kk;
- 11.15.-q;
- 71.10.Pm;
- Field theories in dimensions other than four;
- Gauge field theories;
- Fermions in reduced dimensions;
- High Energy Physics - Theory;
- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect
- E-Print:
- 25 pages, uses JHEP format, young.sty (included). v2: Updated references, typos corrected