Exact Witten Index in D=2 supersymmetric Yang-Mills quantum mechanics
نویسندگان
چکیده
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 spectrum and restricted Witten index of the system with very high precision (taking into account up to 105 quanta). Independently, the exact value of the restricted Witten index is derived analytically for the first time. PACS: 11.10.Kk, 04.60.Kz
منابع مشابه
High precision study of the structure of D = 4 supersymmetric Yang-Mills quantum mechanics
The spectrum of D = 4 supersymmetric Yang-Mills quantum mechanics is computed with high accuracy in all channels of angular momentum and fermion number. Localized and non-localized states coexists in certain channels as a consequence of the supersymmetric interactions with flat valleys. All states fall into well identifiable supermultiplets providing an explicit realization of supersymmetry on ...
متن کاملHamiltonian study of Supersymmetric Yang-Mills Quantum Mechanics
New results obtained within the recently developed approach to supersymmetric quantum mechanical systems are presented. The method does not suffer from the sign problem in any dimensions and is capable to provide any quantum observable with controllable systematic error. Discussed results include: the spectrum and Witten index of the D=4 system, and the spectrum of zero volume glueballs in high...
متن کاملClassical M - Fivebrane Dynamics and Quantum N = 2 Yang - Mills
We obtain the complete quantum Seiberg-Witten effective action for N = 2 supersymmetric SU(N) Yang-Mills theory from the classical M-fivebrane equations of motion with N threebranes moving in its worldvolume.
متن کاملN = 4 super Yang - Mills matrix integrals for almost all simple gauge groups
In this paper the partition function of N = 4 D = 0 super Yang-Mills matrix theory with arbitrary simple gauge group is discussed. We explicitly computed its value for all classical groups of rank r 6 11 and for the exceptional groups G2, F4 and E6. In the case of classical groups of arbitrary rank we conjecture general formulas for the Br, Cr and Dr series in addition to the known result for t...
متن کاملAspects of N T ≥ 2 Topological Gauge Theories and D-branes
We comment on various aspects of topological gauge theories possessing N T ≥ 2 topological symmetry: 1. We show that the construction of Vafa-Witten and Dijkgraaf-Moore of 'bal-anced' topological field theories is equivalent to an earlier construction in terms of N T = 2 superfields inspired by supersymmetric quantum mechanics. 2. We explain the relation between topological field theories calcu...
متن کامل