The bi-conical vector model at $1/N$

Abstract

We study finite $N$ aspects of the $O(m)\times O(N-m)$ vector model with quartic interactions in general $2\le d\le 6$ spacetime dimensions. This model has recently been shown to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in $d=4-\epsilon$ dimensions. The large rank limit of the bi-conical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general $d$. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite $N$. In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only $d$.

35 pages, minor revisions; references updated; accepted for publication to JHEP

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Cited by in corpus (7)

• A model of persistent breaking of discrete symmetry
• A model of persistent breaking of continuous symmetry
• Long-range fermions and critical dualities
• CFT data in the Gross-Neveu model
• Infinite distances in multicritical CFTs and higher-spin holography
• Critical long-range vector model in the UV
• Long-Range Vector Models at Large N