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Ising model andN=2 supersymmetric theories

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Abstract

We establish a direct link between massive Ising model and arbitrary massiveN=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 inN=2 theories. The tau-function appearing in the Ising model (i.e., the spin correlation function) is reinterpreted in theN=2 context as a new “index”. In special cases this new index is related to the Ray-Singer analytic torsion, and can be viewed as a generalization of that to the loop space of Kähler manifolds.

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Authors and Affiliations

  1. International School for Advanced Studies, SISSA-ISAS, Trieste, Italy

    Sergio Cecotti

  2. I.N.F.N., sez. di Trieste, Trieste, Italy

    Sergio Cecotti

  3. Lyman Laboratory of Physics, Harvard University, 02138, Cambridge, MA, USA

    Cumrun Vafa

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  1. Sergio Cecotti
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  2. Cumrun Vafa
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Communicated by R. Dijkgraaf

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Cecotti, S., Vafa, C. Ising model andN=2 supersymmetric theories. Commun.Math. Phys. 157, 139–178 (1993). https://doi.org/10.1007/BF02098023

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