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Critical O(N) models in 6-epsilon dimensions

Author(s): Fei, Lin; Giombi, Simone; Klebanov, Igor R

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Abstract: We revisit the classic O(N) symmetric scalar field theories in d dimensions with interaction (phi(i)phi(i))(2). For 2 < d < 4 these theories flow to the Wilson-Fisher fixed points for any N. A standard large N Hubbard-Stratonovich approach also indicates that, for 4 < d < 6, these theories possess unitary UV fixed points. We propose their alternate description in terms of a theory of N + 1 massless scalars with the cubic interactions sigma phi(i)phi(i) and sigma(3). Our one-loop calculation in 6 - epsilon dimensions shows that this theory has an IR stable fixed point at real values of the coupling constants for N > 1038. We show that the 1/N expansions of various operator scaling dimensions match the known results for the critical O(N) theory continued to d = 6 - epsilon. These results suggest that, for sufficiently large N, there are 5-dimensional unitary O(N) symmetric interacting conformal field theories (CFTs); they should be dual to the Vasiliev higher-spin theory in AdS(6) with alternate boundary conditions for the bulk scalar. Using these CFTs we provide a new test of the 5-dimensional F theorem, and also find a new counterexample for the C-T theorem.
Publication Date: 15-Jul-2014
Electronic Publication Date: 14-Jul-2014
Citation: Fei, Lin, Giombi, Simone, Klebanov, Igor R. (2014). Critical O(N) models in 6-epsilon dimensions. PHYSICAL REVIEW D, 90 (10.1103/PhysRevD.90.025018
DOI: doi:10.1103/PhysRevD.90.025018
ISSN: 2470-0010
EISSN: 2470-0029
Type of Material: Journal Article
Journal/Proceeding Title: PHYSICAL REVIEW D
Version: Final published version. This is an open access article.

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