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Vacuum Structure of Two-Dimensional $ϕ^4$ Theory on the Orbifold $S^{1}/Z_{2}$

H. T. Cho
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Abstract

We consider the vacuum structure of two-dimensional $ϕ^4$ theory on $S^{1}/Z_{2}$ both in the bosonic and the supersymmetric cases. When the size of the orbifold is varied, a phase transition occurs at $L_{c}=2π/m$, where $m$ is the mass of $ϕ$. For $L L_{c}$, there are two degenerate vacua. We also obtain the 1-loop quantum corrections around these vacuum solutions, exactly in the case of $L L_{c}$. As for the quantum corrections, the fermionic contributions cancel the singular part of the bosonic contributions at L=0. Then the total quantum correction has a minimum at the critical length $L_{c}$.

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H. T. Cho. 2005-07-19. Vacuum Structure of Two-Dimensional $ϕ^4$ Theory on the Orbifold $S^{1}/Z_{2}$. https://doi.org/10.1103/physrevd.72.065010

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