Abstract
Abstract
In this paper we examine analytically the large-N gap equation and its solution for the 2D ℂℙ
N −1 sigma model defined on a Euclidean spacetime torus of arbitrary shape and size (L, β), β being the inverse temperature. We find that the system has a unique homogeneous phase, with the ℂℙ
N −1 fields n
i
acquiring a dynamically generated mass (λ) ≥ Λ2 (analogous to the mass gap of SU(N ) Yang-Mills theory in 4D), for any β and L. Several related topics in the recent literature are discussed. One concerns the possibility, which turns out to be excluded according to our analysis, of a “Higgs-like” — or deconfinement — phase at small L and at zero temperature. Another topics involves “soliton-like” (inhomogeneous) solutions of the generalized gap equation, which we do not find. A related question concerns a possible instability of the standard ℂℙ
N −1 vacuum on R2, which is shown not to occur. In all cases, the difference in the conclusions can be traced to the existence of certain zeromodes and their proper treatment. The ℂℙ
N −1 model with twisted boundary conditions is also analyzed. The θ dependence and different limits involving N , β and L are briefly discussed.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference53 articles.
1. A. D’Adda, M. Lüscher and P. Di Vecchia, A 1/n Expandable Series of Nonlinear σ-models with Instantons, Nucl. Phys.B 146 (1978) 63 [INSPIRE].
2. E. Witten, Instantons, the Quark Model and the 1/n Expansion, Nucl. Phys.B 149 (1979) 285 [INSPIRE].
3. H. Eichenherr, SU(N ) Invariant Nonlinear σ-models, Nucl. Phys.B 146 (1978) 215 [Erratum ibid.B 155 (1979) 544] [INSPIRE].
4. V.L. Golo and A.M. Perelomov, Solution of the Duality Equations for the Two-Dimensional SU(N ) Invariant Chiral Model, Phys. Lett.B 79 (1978) 112 [INSPIRE].
5. V.A. Fateev, I.V. Frolov and A.S. Schwarz, Quantum Fluctuations of Instantons in Two-dimensional Nonlinear Theories, Sov. J. Nucl. Phys.30 (1979) 590 [INSPIRE].
Cited by
7 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献