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A Three-Dimensional Conformal Field Theory

S. Guruswamy·S. G. Rajeev·P. Vitale
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Abstract

This talk is based on a recent paper$^{1}$ of ours. In an attempt to understand three-dimensional conformal field theories, we study in detail one such example --the large $N$ limit of the $O(N)$ non-linear sigma model at its non-trivial fixed point -- in the zeta function regularization. We study this on various three-dimensional manifolds of constant curvature of the kind $Σ\times R$ ($Σ=S^1 \times S^1, S^2, H^2$). This describes a quantum phase transition at zero temperature. We illustrate that the factor that determines whether $m=0$ or not at the critical point in the different cases is not the `size' of $Σ$ or its Riemannian curvature, but the conformal class of the metric.

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S. Guruswamy, S. G. Rajeev, P. Vitale. 1994-08-04. A Three-Dimensional Conformal Field Theory. https://arxiv.org/abs/cond-mat/9408018

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