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arXiv · 1608.00262

The universal coefficient of the exact correlator of a large-$N$ matrix field theory

Eytan Katzav·Peter Orland
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Abstract

Exact expressions have been proposed for correlation functions of the large-$N$ (planar) limit of the $(1+1)$-dimensional ${\rm SU}(N)\times {\rm SU}(N)$ principal chiral sigma model. These were obtained with the form-factor bootstrap. The short-distance form of the two-point function of the scaling field $\Phi(x)$, was found to be $N^{-1}\langle {\rm Tr}\,\Phi(0)^{\dagger} \Phi(x)\rangle=C_{2}\ln^{2}mx$, where $m$ is the mass gap, in agreement with the perturbative renormalization group. Here we point out that the universal coefficient $C_{2}$, is proportional to the mean first-passage time of a L\'{e}vy flight in one dimension. This observation enables us to calculate $C_{2}=1/16\pi$.

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Eytan Katzav, Peter Orland. 2016-07-31. The universal coefficient of the exact correlator of a large-$N$ matrix field theory. https://doi.org/10.1103/physrevd.94.065041

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