Six dimensional Landau-Ginzburg-Wilson theory

Abstract

We renormalize the six dimensional cubic theory with an $O(N)$ $\times$ $O(m)$ symmetry at three loops in the modified minimal subtraction (MSbar) scheme. The theory lies in the same universality class as the four dimensional Landau-Ginzburg-Wilson model. As a check we show that the critical exponents derived from the three loop renormalization group functions at the Wilson-Fisher fixed point are in agreement with the large $N$ $d$-dimensional critical exponents of the underlying universal theory. Having established this connection we analyse the fixed point structure of the perturbative renormalization group functions to estimate the location of the conformal window of the $O(N)$ $\times$ $O(2)$ model.

arXiv comment36 latex pages, 2 tables, anc directory contains txt file with electronic version of renormalization group functions

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• Analytic and Numerical Bootstrap of CFTs with $O(m)\times O(n)$ Global Symmetry in 3D
• Leading order CFT analysis of multi-scalar theories in d>2
• Renormalization-Group Behavior of ${\varphi }^3$ Theories in $d=6$ Dimensions
• The two upper critical dimensions of the Ising and Potts models
• Bifundamental Multiscalar Fixed Points in $d=3-\epsilon$