Flow equation for the scalar model in the large $N$ expansion and its applications

Understand

We study the flow equation of the O($N$) $\varphi^4$ model in $d$ dimensions at the next-to-leading order (NLO) in the $1/N$ expansion.

• Using the Schwinger-Dyson equation, we derive 2-pt and 4-pt functions of flowed fields.
• As the first application of the NLO calculations, we study the running coupling defined from the connected 4-pt function of flowed fields in the $d+1$ dimensional theory.
• We show in particular that this running coupling has not only the UV fixed point but also an IR fixed point (Wilson-Fisher fixed point) in the 3 dimensional massless scalar theory.