Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-01-16
Nucl.Phys. B470 (1996) 369-395
Physics
High Energy Physics
High Energy Physics - Theory
31 pages, 2 PostScript figures, TeX + epsf.tex
Scientific paper
10.1016/0550-3213(96)00168-X
The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to \infty$ while the coupling $g \to g_c$ in a correlated manner (the double scaling limit) a massless bound state $O(N)$ singlet is formed and powers of $1/N$ are compensated by IR singularities. The persistence of the $N \to \infty$ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.
Eyal Galit
Moshe Maayan
Nishigaki Shinsuke
Zinn-Justin Jean
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