The universal coefficient of the exact correlator of a large-$N$ matrix   field theory
  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 $C_{2}=1/16\pi$. 
Eytan Katzav (Racah Inst, Jerusalem) and Peter Orland (Bohr Inst.,   Baruch College of CUNY, Graduate Center of CUNY)
hep-th cond-mat.dis-nn cond-mat.stat-mech hep-lat math-ph math.MP