Three loop analysis of the critical O (N) models in 6-ε dimensions

By L. Fei, S. Giombi, I. Klebanov, G. Tarnopolsky. 2014

178 citations recorded by the source corpus.

We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2 \sigma^3$. We calculate the 3-loop beta functions for the two couplings and use them to determine certain operator scaling dimensions at the IR stable fixed point up to order $\epsilon^3$. We also use the beta functions to determine the corrections to the critical value of $N$ below which there is no fixed point at real couplings. The result suggests a very significant reduction in the critical value as the dimension is decreased to $5$. We also study the theory with $N=1$, which has a $Z_2$ symmetry under $\phi\rightarrow -\phi$. We show that it possesses an IR stable fixed point at imaginary couplings which can be reached by flow from a nearby fixed point describing a pair of $N=0$ theories. We calculate certain operator scaling dimensions at the IR fixed point of the $N=1$ theory and suggest that, upon continuation to two dimensions, it describes a non-unitary conformal minimal model.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/000b64e13b0b2524dfc0ab47c06f28e6ab494263

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Nuclear and High Energy Physics

  1. S. Giombi
  2. I. Klebanov
  3. Xi Yin
  4. M. Gaberdiel
  5. Rajesh Gopakumar
  6. O. Aharony
  7. E. D. Skvortsov
  8. A. Tseytlin

Citations in the corpus