Graphical expansion of the partition function for the supersymmetric non-linear σ-model in (1+0) D
Schambach, M.
In the present work, a graphical evolution of the fermionic part of the state sum of the supersymmetric nonlinear σ-model in (1 + 0) dimensions is presented. It is shown that only closed, non-contractible and non-returning, one- to (N-1) stranded graphs, which do not intersect each other, contribute to the state sum. The weight of a graph is worked out in closed form using a point weight defined for each flavor and location of the lattice. The integration of the auxiliary σ-field introduced by the Hubbard-Stratonovich transform is given for all possible cases. In contrast, a possible analytical treatment of the integration of the bosonic fields, e.g. in the form of a further graphical development, is only hinted at and reference is made to a Monte-Carlo simulation.