Dimensionally reduced SYM at large-: an intriguing Coulomb approximation
Nov, 2010
30 pages
Published in:
- JHEP 06 (2011) 051
e-Print:
- 1011.1200 [hep-th]
Report number:
- CERN-PH-TH-2010-240,
- IFUP-TH-2010-37,
- TPJU-3-2010,
- MPI-2010-137
Citations per year
Abstract: (arXiv)
We consider the light-cone (LC) gauge and LC quantization of the dimensional reduction of super Yang Mills theory from four to two dimensions. After integrating out all unphysical degrees of freedom, the non-local LC Hamiltonian exhibits an explicit supersymmetry. A further SUSY-preserving compactification of LC-space on a torus of radius , allows for a large- numerical study where the smooth large- limit of physical quantities can be checked. As a first step, we consider a simple, yet quite rich, "Coulomb approximation" that maintains an subgroup of the original supersymmetry and leads to a non-trivial generalization of 't Hooft's model with an arbitrary --but conserved-- number of partons. We compute numerically the eigenvalues and eigenvectors both in momentum and in position space. Our results, so far limited to the sectors with 2, 3 and 4 partons, directly and quantitatively confirm a simple physical picture in terms of a string-like interaction with the expected tension among pairs of nearest-neighbours along the single-trace characterizing the large- limit. Although broken by our approximation, traces of the full supersymmetry are still visible in the low-lying spectrum.Note:
- 30 pages, 13 figures, Footnote page 3 replaced, Note Added at the end, 4 References added
- Supersymmetric gauge theory
- Confinement
- Field Theories in Lower Dimensions
- 1/N Expansion
- gauge field theory: Yang-Mills: supersymmetry
- supersymmetry: 4
- quantization: light cone
- Hamiltonian formalism: light cone
- Coulomb
- parton
References(0)
Figures(16)
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