Abstract
If the space of minima of the effective potential of a weakly coupled 2d quantum field theory is not connected, then a mass gap will be nonpertubatively generated. As examples, we consider two sigma models compactified on a small circle with twisted boundary conditions. In the compactified SO(3) model the vacuum manifold consists of two points and the mass gap is nonperturbative. In the case of the compactified SU(2) principal chiral model the vacuum manifold is a single circle and the mass gap is perturbative.
Highlights
We consider two σ models compactified on a small circle with twisted boundary conditions
In the compactified CP1 model, the vacuum manifold consists of two points and the mass-gap is nonperturbative
A similar half-charged excitation appears to cause the mass-gap in the SU(2) principal chiral model (PCM), where the Euclidean theory has no topologically stable solutions
Summary
If the space of minima of the effective potential of a weakly coupled 2d quantum field theory is not connected, a mass-gap will be nonperturbatively generated. We consider two σ models compactified on a small circle with twisted boundary conditions. In the compactified CP1 model, the vacuum manifold consists of two points and the mass-gap is nonperturbative.
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