Vacuum energy of the supersymmetric CPN-1 model on R × S1 in the 1/N expansion

Kosuke Ishikawa, Morikawa Okuto, Kazuya Shibata, Hiroshi Suzuki

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7 Citations (Scopus)


By employing the 1/N expansion, we compute the vacuum energy E(δε) of the two-dimensional supersymmetric (SUSY) CPN-1 model on R × S1 with ZN 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 S1, 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 ΛR as Λ∼ e-2π/ΛR, 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 ΛR,.

Original languageEnglish
Article number063B02
JournalProgress of Theoretical and Experimental Physics
Issue number6
Publication statusPublished - Jun 8 2020

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


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