... 1
E-mail address: ansoldi@trieste.infn.it 
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... Castro2
E-mail address: castro@ctsps.cau.edu 
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...E.Spallucci3
E-mail address: spallucci@vstst0.ts.infn.it 
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... theory4
It is important to remark that we are not attempting a WWM quantization of the classical quenched field theory, but we are only deforming the Lie algebraic structure. 
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... restrict5
In two dimensions every metric is conformally flat. In our case, i.e. four dimensions, we need to require conformal flatness. 
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... with6
It can be useful to list the dimensions in natural units of various quantities. The main reason is that quenched, dimensional reduced, gauge variables have not canonical dimensions:
    $\displaystyle \left[\,{\mbox{\boldmath{$D$}}}_\mu\,\right]= \left[\,{\cal A }_\... ...] = (\,length\,)\ , \qquad \left[\,{\cal F }_{\mu\nu}\,\right]= (\,length\, )^2$  
    $\displaystyle \left[\,X^\mu\,\right]= (\, length\,)$  
    $\displaystyle \left[\,a\,\right]= length\ ,\qquad \left[\,\Lambda\,\right]= (\,length\,)^{-1}$  
    $\displaystyle \left[\,\sigma^m\,\right]=1 \ ,\qquad \left[\, \left\{\, X^\mu\ , X^\nu\, \right\}_{PB}\,\right]=(\, length\,)^2$  
    $\displaystyle \left[\,\mu_0\,\right]= (\, length\,)^{-1}\ ,\qquad \left[\,\kappa\,\right]= (\, length\,)^{-4}$ (26)

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