Two-dimensional N = (2,2) super Yang-Mills theory on the lattice via dimensional reduction

Jul, 2005
19 pages
Published in:
  • JHEP 10 (2005) 082
e-Print:
Report number:
  • IU-MSTP-70,
  • RIKEN-TH-48,
  • ITHEP-507,
  • UTCCS-P-14

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Abstract:
The N=(2,2) extended super Yang-Mills theory in 2 dimensions is formulated on the lattice as a dimensional reduction of a 4 dimensional lattice gauge theory. We use the plaquette action for a bosonic sector and the Wilson- or the overlap-Dirac operator for a fermion sector. The fermion determinant is real and, moreover, when the overlap-Dirac operator is used, semi-positive definite. The flat directions in the target theory become compact and present no subtlety for a numerical integration along these directions. Any exact supersymmetry does not exist in our lattice formulation: nevertheless we argue that one-loop calculable and finite mass counter terms ensure a supersymmetric continuum limit to all orders of perturbation theory.
  • lattice field theory: action
  • gauge field theory: Yang-Mills
  • supersymmetry
  • dimension: 2
  • dimensional reduction
  • operator: Dirac
  • fermion: determinant
  • effective potential: flat direction
  • mass: finite
  • continuum limit