CP(N) sigma model on a finite interval revisited

Abstract

In this short note we will revisit the large $N$ solution of $\mathbb{C}{P}^N$ sigma model on a finite interval of length $L$. We will find a family of boundary conditions for which the large $N$ saddle point can be found analytically. For a certain choice of the boundary conditions the theory has only one phase for all values of $L$. Also, we will provide an example when there are two phases: for large $L$ there is a standard phase with an unbroken $U(1)$ gauge symmetry and for small $L$ there is Higgs phase with a broken gauge symmetry.

7 pages

References in corpus (4)

• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• CP(N-1) model on finite interval in the large N limit
• Non-Abelian String of a Finite Length
• Monopole-vortex complex at large distances and nonAbelian duality

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