Ising Model and N = 2 Supersymmetric Theories
Sergio Cecotti,Cumrun Vafa +1 more
TL;DR: In this article, a direct link between massive Ising model and arbitrary massive N = 2 supersymmetric QFT's in two dimensions is established, which 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.
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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 Kahler manifolds.
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Citations
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References
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TL;DR: In this article, the exact functional dependence of Δa(U) on any untwisted modulus field U of an orbifold vacuum was derived, where Aa is easily computable rational constants.
From Form Factors to Correlation Functions: The Ising Model
Olivier Babelon,Denis Bernard +1 more
TL;DR: In this article, it was shown that the spin-spin and disorder-disorder correlation functions are governed by the Painleve III nonlinear differential equation, and that the generating function of the correlation functions of the descendents of the spin and disorder operators is an N -soliton, N → ∞, τ-funtion of the sinh-Gordon hierarchy.
Functional Measure, Topology and Dynamical Supersymmetry Breaking
S. Cecotti,L. Girardello +1 more
TL;DR: In this paper, a functional interpretation of Witten's criterion for supersymmetry breaking is presented, and a functional representation of the index Δ and its properties are discussed. And a topological explanation of Δs as the winding number of a functional mapping introduced by Nicolai is given.
Topological sigma models
TL;DR: A variant of the usual supersymmetric nonlinear sigma model is described in this article, governing maps from a Riemann surface to an arbitrary almost complex manifold, which possesses a fermionic BRST-like symmetry, conserved for arbitrary Σ, and obeying Q 2 = 0.