Flow equation for the scalar model in the large N expansion and its applications
Abstract
We study the flow equation of the O(N) φ^4 model in d dimensions at the nexttoleading order (NLO) in the 1/N expansion. Using the SchwingerDyson equation, we derive 2pt and 4pt functions of flowed fields. As the first application of the NLO calculations, we study the running coupling defined from the connected 4pt function of flowed fields in d+1dimensional theory. We show in particular that this running coupling has not only an ultraviolet fixed point but also an infrared fixed point (WilsonFisher fixed point) in 3dimensional massless scalar theory. As the second application, we calculate the NLO correction to the induced metric in d+1 dimensions with d=3 in the massless limit. While the induced metric describes a 4dimensional Euclidean AntideSitter (AdS) space at the leading order, as shown in the previous paper, the NLO corrections make the space asymptotically AdS only in the UV and IR limits. Remarkably, while the AdS radius does not receive an NLO correction in the UV limit, the AdS radius decreases at the NLO in the IR limit, which corresponds to the WilsonFisher fixed point in the original scalar model in 3 dimensions.
 Publication:

Progress of Theoretical and Experimental Physics
 Pub Date:
 April 2017
 DOI:
 10.1093/ptep/ptx025
 arXiv:
 arXiv:1701.00046
 Bibcode:
 2017PTEP.2017d3B01A
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Lattice
 EPrint:
 39 pages