Casimir Force for the $\mathbb{C}{P}^{N-1}$ Model

Abstract

In this work, we derive exact self-consistent solutions to the gap equations of the $\mathbb{C}{P}^{N-1}$ model on a finite interval with Dirichlet boundary conditions in the large-$N$ approximation. The solution reproduce the confining phase in the infinite system by taking the appropriate limit. We compute the vacuum energy and the Casimir force and observe that the sign of the force is always attractive.

6 pages, 3 figures. Updates in v2: fig.3 corrected, minor typos corrected. v3: published version

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Cited by in corpus (14)

• The Casimir effect and deconfinement phase transition
• Boundary states and Non-Abelian Casimir effect in lattice Yang-Mills theory
• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Casimir boundaries, monopoles, and deconfinement transition in 3+1 dimensional compact electrodynamics
• Nonperturbative Casimir Effects in Field Theories: aspects of confinement, dynamical mass generation and chiral symmetry breaking
• Nonlinear dynamical Casimir effect at weak nonstationarity
• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• Spin Statistics and Surgeries of Topological Solitons in QCD Matter in Magnetic Field
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model
• Confinement and XSB in QCD: Mysteries and beauty of soliton dynamics in nonAbelian gauge theories
• CP(N) model on regions with boundary
• One-loop effective action of the $\mathbb{C}{P}^{N-1}$ model at large $\mu \beta$