2003/04/15 by Fred Cooper, Pasquale Sodano, Andrea Trombettoni +1
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons #hep-th
paper · pdf · doi:10.1103/physrevd.68.045011
published as Phys.Rev. D68 (2003) 045011 · 21 pages, Latex (Revtex4) v3:minor grammatical changes and additions
arxiv created 2003/04/15 · openalex publication_date 2003/08/28 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We discuss an O(N) symmetric extension of the sine-Gordon (SG) equation which, using a path integral approach, allows for an expansion around the leading order in large N (Gaussian) approximation. The model is described by the Lagrangian L=(1)/(2)(\ensuremath∂_\ensuremathμ\stackrel\ensuremath→\ensuremathφ)2+N(\ensuremathα0/\ensuremathβ2)cos\ensuremathβ√\ensuremathρ, with \ensuremathρ=(\stackrel\ensuremath→\ensuremathφ\ensuremath⋅\stackrel\ensuremath→\ensuremathφ)/N. At the leading order we show that the results of our approach agree with the ones of a large-N variational computation. We discuss the striking differences arising for a nonpolynomial interaction between the large-N form for 〈V[\ensuremathφ]〉 in the Gaussian approximation and the N=1 case; when V[\ensuremathφ] is a polynomial no such drastic differences occur. We find that, for our large-N extension of the sine-Gordon model, the unbroken ground state is unstable as one increases the coupling constant (as it is for the original SG equation) and we find in leading order that the unbroken symmetry vacuum is stable as long as \ensuremathβ2<~24\ensuremathπ.