Action of hedgehog instantons in the disordered phase of the (2 + 1)-dimensional CPN-1 model

Ganpathy Murthy, Subir Sachdev

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109 Scopus citations

Abstract

The large-N limit of the (2 + 1)-dimensional CPN-1 model exhibits hedgehog-like instanton saddle points in its disordered phase. We determine the structure of these saddle points and evaluate the action, Score, of a charge-q instanton. We find that lim ξ a → ∞ limN → ∞ Sscore N = 2ρ{variant}qln( ξ a), where the order of limits is significant. Here a is the lattice spacing, ξ is the spin correlations length, and ρ{variant}q are a set of universal constants: ρ{variant}1 = 0.062296..., ρ{variant}2 = 0.155548.... Free charge-q instantons therefore occur with a density ∼ a -3( ξ a)-2Nρ{variant}q in the disodered phase. Moreover, the length scale, ξC, with which correlations of U(1) gauge field, Aμ, decay exponentially, is ξC ∼ a( ξ a)Nρ{variant}1. The length ξC is also the scale at which the matter fields, zα, experience a confining linear potential. Consequences for spin-Peierls ordering in two-dimensional quantum SU(N) antiferromagnets will be discussed elsewhere, and are briefly noted for completeness.

Original languageEnglish
Pages (from-to)557-595
Number of pages39
JournalNuclear Physics B
Volume344
Issue number3
DOIs
StatePublished - Nov 19 1990

Bibliographical note

Funding Information:
We would like to thank T. Applequist, S. Chakravarty, J.B. Marston, N. Read, R. Shankar, and C. Sommerfield for useful discussions. One of us (S.S.) is indebted to N. Read for a collaboration \[7—9w\] hich gave rise to many of the questions addressed in this paper. In particular it was the insistence by N. Read that the core-action was poorly understood and his pointing out of the relevance of the Wu—Yang solution \[19\]which lead to S.S.’s study of this problem. R. Shankar introduced us to the important results of ‘t Hooft and clarified our understanding of confinement in the CP”~model \[1254\,].The research of S.S. was supported in part by National Science Foundation grant no. DMR 8857228 and by the Alfred P. Sloan Foundation. G.M. was supported by National Science Foundation grant no. PHY 89-08495.

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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