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Free fermion and Seiberg–Witten differential in random plane partitions
- Source :
- Nuclear Physics B. 715:275-303
- Publication Year :
- 2005
- Publisher :
- Elsevier BV, 2005.
-
Abstract
- A model of random plane partitions which describes five-dimensional $\mathcal{N}=1$ supersymmetric SU(N) Yang-Mills is studied. We compute the wave functions of fermions in this statistical model and investigate their thermodynamic limits or the semi-classical behaviors. These become of the WKB type at the thermodynamic limit. When the fermions are located at the main diagonal of the plane partition, their semi-classical wave functions are obtained in a universal form. We further show that by taking the four-dimensional limit the semi-classical wave functions turn to live on the Seiberg-Witten curve and that the classical action becomes precisely the integral of the Seiberg-Witten differential. When the fermions are located away from the main diagonal, the semi-classical wave functions depend on another continuous parameter. It is argued that they are related with the wave functions at the main diagonal by the renormalization group flow of the underlying gauge theory.<br />Comment: 32 pages, 3 figures, typos corrected
- Subjects :
- High Energy Physics - Theory
Physics
Nuclear and High Energy Physics
Plane (geometry)
Plane partition
FOS: Physical sciences
Mathematical Physics (math-ph)
Supersymmetry
Fermion
Main diagonal
WKB approximation
High Energy Physics - Theory (hep-th)
Quantum mechanics
Thermodynamic limit
Gauge theory
Mathematical Physics
Mathematical physics
Subjects
Details
- ISSN :
- 05503213
- Volume :
- 715
- Database :
- OpenAIRE
- Journal :
- Nuclear Physics B
- Accession number :
- edsair.doi.dedup.....731e12e6e4ca2130c63a472843682864