Exact Witten index in D = 2 supersymmetric Yang-Mills quantum mechanics

Sep, 2002
13 pages
Published in:
  • Phys.Lett.B 550 (2002) 121-127
e-Print:
Report number:
  • TPJU-15-02,
  • IFUP-TH-2002-36,
  • MPI-PHT-2002-45

Citations per year

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Abstract:
A new, recursive method of calculating matrix elements of polynomial hamiltonians is proposed. It is particularly suitable for the recent algebraic studies of the supersymmetric Yang-Mills quantum mechanics in any dimensions. For the D=2 system with the SU(2) gauge group, considered here, the technique gives exact, closed expressions for arbitrary matrix elements of the hamiltonian and of the supersymmetric charge, in the occupation number representation. Subsequent numerical diagonalization provides the spectrum and restricted Witten index of the system with very high precision (taking into account up to 10510^5 quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time.
Note:
  • 13 pages, 1 figure Report-no: TPJU-15/02, IFUP-TH/2002-36, MPI-PhT/2002-45
  • 11.10.Kk
  • 04.60.Kz
  • Matrix model
  • Quantum mechanics
  • Non-Abelian gauge theories
  • quantum mechanics
  • gauge field theory: SU(2)
  • dimension: 2
  • supersymmetry
  • Hamiltonian formalism