The spectrum of the anomalous dimensions of the composite operators in the $\epsilon$ - expansion in the scalar ${\varphi }^4$ - field theory

Abstract

The spectrum of the anomalous dimensions of the composite operators (with arbitrary number of fields $n$ and derivatives $l$) in the scalar ${\varphi }^4$ - theory in the first order of the $\epsilon$ -expansion is investigated. The exact solution for the operators with number of fields $\le 4$ is presented. The behaviour of the anomalous dimensions in the large $l$ limit has been analyzed. It is given the qualitative description of the %structure of the spectrum for the arbitrary $n$.

25 pages, latex, a few changes in latex commands

References in corpus (3)

• The spectrum of critical exponents in $({\vec{\varphi }}^2{)}^2$-theory in $d=4-\eps$ dimensions -- Resolution of degeneracies and hierarchical structures
• The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions
• The critical O($N$) $\sigma$-model at dimension $2<d<4$: Hardy-Ramanujan distribution of quasi-primary fields and a collective fusion approach

Cited by in corpus (6)

• The critical O(N) CFT: Methods and conformal data
• Evolution equations beyond one loop from conformal symmetry
• Revisiting the dilatation operator of the Wilson-Fisher fixed point
• Leading Order Anomalous Dimensions at the Wilson-Fisher Fixed Point from CFT
• High-gradient operators in the N-vector model
• Generic scaling relation in the scalar ${\varphi }^4$ model