## Abstract

By employing the 1/N expansion, we compute the vacuum energy E(δε) of the two-dimensional supersymmetric (SUSY) CP^{N-1} model on R × S^{1} with Z_{N} twisted boundary conditions to the second order in a SUSY-breaking parameter δε. This quantity was vigorously studied recently by Fujimori et al. using a semi-classical approximation based on the bion, motivated by a possible semi-classical picture on the infrared renormalon. In our calculation, we find that the parameter δε receives renormalization and, after this renormalization, the vacuum energy becomes ultraviolet finite. To the next-to-leading order of the 1/N expansion, we find that the vacuum energy normalized by the radius of the S^{1}, R, RE(δε) behaves as inverse powers of Λ R for Λ R small, where Λ is the dynamical scale. Since Λ is related to the renormalized 't Hooft coupling Λ_{R} as Λ∼ e-2π/Λ_{R}, to the order of the 1/N expansion we work out, the vacuum energy is a purely non-perturbative quantity and has no well-defined weak coupling expansion in Λ_{R},.

Original language | English |
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Article number | 063B02 |

Journal | Progress of Theoretical and Experimental Physics |

Volume | 2020 |

Issue number | 6 |

DOIs | |

Publication status | Published - Jun 8 2020 |

## All Science Journal Classification (ASJC) codes

- General Physics and Astronomy

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