The bi-conical vector model at 1/N

Abstract

We study finite N aspects of the O(m) × O(N − m) vector model with quartic interactions in general 2 ≤ d ≤ 6 spacetime dimensions. This model has recently been shown [1, 2] to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in d = 4 − ϵ dimensions. The large rank limit of the biconical 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.

Long-range vector models at large N

“…where µ is IR mass scale [32,33]. The second contribution to σ 2 σ 2 at the next-to-leading order in 1/N is due to insertions of two cubic σ vertices into the leading order diagram:…”

A model of persistent breaking of continuous symmetry

“…The phenomenon of persistent symmetry breaking (PSB), i.e., spontaneous breaking of a global symmetry that persists at arbitrarily high temperatures, was first noticed by Weinberg [2]. Since then it has been actively discussed in cosmology [3][4][5][6][7][8], quantum field theory [1,[9][10][11][12][13][14][15][16] and holography [17][18][19][20][21][22][23][24].…”

“…Thus, during the last year a number of papers studied critical points of the bi-conical O(m) × O(N − m) model in the context of the PSB. At finite temperature T , these models exhibit spontaneous symmetry breaking, and because of scale-invariance symmetry breaking persists to an arbitrarily high T [1,[11][12][13]. Furthermore, the authors of [14,16] constructed critical gauge theory models in 3 + 1 dimensions which exhibit symmetry breaking at arbitrary high temperatures in the infinite N limit.…”

“…2 At the same time, full conformal invariance of the critical bi-conical long-range O(m) × O(N − m) model is less understood. Full conformal symmetry, if present, would restrict the functional form of the three-point functions of primary operators, and ensure that cross-correlators 1 This is to be contrasted with the earlier models of PSB [11][12][13], that studied the local bi-conical O(m) × O(N − m) vector models, where continuous symmetry breaking can occur only in non-integer dimensions 3 < d < 4. The latter choice of dimension, however, raises the issue of unitarity [34].…”

Critical long-range vector model in the UV

“…Importance of matching full CFT data, including sub-leading contributions to the OPE coefficients, in the context of testing critical duality of vector models was recently emphasized in[29].14 See[31,32] for other recent work on persistent symmetry breaking in vector models.…”