Theta-vacuum and large N limit in CP^{N-1} sigma models

Abstract

The theta dependence of the vacuum energy density in CP^{N-1} models is re-analysed in the semiclassical approach, the 1/N expansion and arguments based on the nodal structure of vacuum wavefunctionals. The 1/N expansion is shown not to be in contradiction with instanton physics at finite (spacetime) volume V. The interplay of large volume V and large N parameter gives rise to two regimes with different theta dependence, one behaving as a dilute instanton gas and the other dominated by the traditional large N picture, where instantons reappear as resonances of the one-loop effective action, even in the absence of regular instantonic solutions. The realms of the two regimes are given in terms of the mass gap m by m^2 V << N and m^2 V >> N, respectively. The small volume regime m^2 V << N is relevant for physical effects associated to the physics of the boundary, like the leading role of edge states in the quantum Hall effect, which, however, do not play any role in the thermodynamic limit at large N. Depending on the order in which the limits N -> \infty and V -> \infty are taken, two different theories are obtained; this is the hallmark of a phase transition at 1/N = 0.

arXiv commentv2: 25 pages, 4 eps figures, introduction expanded, matches published version

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Cited by in corpus (10)

• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Topological properties of $C{P}^{N-1}$ models in the large-$N$ limit
• Large-$N$ expansion and $\theta$-dependence of $2d$ $C{P}^{N-1}$ models beyond the leading order
• Flag manifold sigma models: spin chains and integrable theories
• Lattice determination of the topological susceptibility slope ${\chi }^{\prime }$ of $2d{\mathrm{CP}}^{N-1}$ models at large $N$
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• The CP(N-1) model on a Disc and Decay of a Non-Abelian String
• Renormalization of the Nonlinear O(3) Model with Theta-Term
• Large $\theta$ angle in two-dimensional large $N$ ${\mathbb{CP}}^{N-1}$ model