According to Mankowski flat space dimensions We can write, 
$$L= \int \text{dt} \text d^d{x} \left[ \frac{1}{2} \dot\phi^2 - \frac{1}{2}  \left(\frac{\partial \phi}{\partial r} \right)^2 -V(\phi)\right] \tag{1}$$
Where V can be written as $$V = \frac{1}{8} \phi^2 (\phi-2)^2$$

But [the author][1] wrote in his article in the equation (1) including dimensions. 
$$V= \frac{1}{2} m^2 \phi^2+ \frac{\lambda_3}{3!}m^\frac{5-d}{2} \phi^3+ \frac{\lambda_4}{4!}m^{3-d} \phi^4$$

My question s how the dimensions incorporated with the potential? 

  [1]: http://arxiv.org/abs/1003.3459