Ising Model and $N=2$ Supersymmetric Theories

Details Ising Model and $N=2$ Supersymmetric Theories Ising Model and $N=2$ Supersymmetric Theories

1992-09-22

arxiv.org/abs/hep-th/9209085v1

Commun.Math.Phys. 157 (1993) 139-178

Physics

High Energy Physics

High Energy Physics - Theory

60 pages, HUTP-92/A044,SISSA-167/92/EP

Scientific paper

10.1007/BF02098023

We establish a direct link between massive Ising model and arbitrary massive $N=2$ supersymmetric QFT's in two dimensions. This explains why the equations which appear in the computation of spin-correlations in the non-critical Ising model are the same as those describing the geometry of vacua in $N=2$ theories. The tau-function appearing in the Ising model (i.e., the spin correlation function) is reinterpreted in the $N=2$ context as a new `index'. In special cases this new index is related to Ray-Singer analytic torsion, and can be viewed as a generalization of that to loop space of K\"ahler manifolds.

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