Conserved currents, consistency relations, and operator product expansions in the conformally invariant \(O(N)\) vector model

DOI10.1006/APHY.1996.0068zbMATH Open0873.47044arXivhep-th/9410093OpenAlexW2035534832MaRDI QIDQ1355137

Author name not available (Why is that?)

Publication date: 17 June 1997

Published in: (Search for Journal in Brave)

Abstract: We discuss conserved currents and operator product expansions (OPE's) in the context of a $O(N)$ invariant conformal field theory. Using OPE's we find explicit expressions for the first few terms in suitable short-distance limits for various four-point functions involving the fundamental $N$-component scalar field $ph{i}^{alpha}(x)$, $alpha=1,2,\mathrm{..},N$. We propose an alternative evaluation of these four-point functions based on graphical expansions. Requiring consistency of the algebraic and graphical treatments of the four-point functions we obtain the values of the dynamical parameters in either a free theory of $N$ massless fields or a non-trivial conformally invariant $O(N)$ vector model in $2<d<4$, up to next-to-leading order in a $1/N$ expansion. Our approach suggests an interesting duality property of the critical $O(N)$ invariant theory. Also, solving our consistency relations we obtain the next-to-leading order in $1/N$ correction for $C_T$ which corresponds to the normalisation of the energy momentum tensor two-point function.

Full work available at URL: https://arxiv.org/abs/hep-th/9410093

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Conserved currents, consistency relations, and operator product expansions in the conformally invariant \(O(N)\) vector model

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1355137)