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On the limiting procedure by which $SDiff(T^2)$ and $SU(\infty)$ are associated

John Swain
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Abstract

There have been various attempts to identify groups of area-preserving diffeomorphisms of 2-dimensional manifolds with limits of SU(N) as $N\to\infty$. We discuss the particularly simple case where the manifold concerned is the two-dimensional torus $T^2$ and argue that the limit, even in the basis commonly used, is ill-behaved and that the large-N limit of SU(N) is much larger than $SDiff(T^2)$.

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John Swain. 2004-05-01. On the limiting procedure by which $SDiff(T^2)$ and $SU(\infty)$ are associated. https://arxiv.org/abs/hep-th/0405002

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