TY - JOUR

T1 - Vacuum energy of the supersymmetric CPN-1 model on R × S1 in the 1/N expansion

AU - Ishikawa, Kosuke

AU - Okuto, Morikawa

AU - Shibata, Kazuya

AU - Suzuki, Hiroshi

N1 - Funding Information:
We are grateful to Akira Nakayama and Hiromasa Takaura for collaboration at various stages of this work. We would also like to thank Toshiaki Fujimori, Tatsuhiro Misumi, Norisuke Sakai, and Kazuya Yonekura for helpful discussions. This work was supported by JSPS Grants-in-Aid for Scientific Research numbers JP18J20935 (O.M.) and JP16H03982 (H.S.).
Publisher Copyright:
© 2020 The Author(s). Published by Oxford University Press on behalf of the Physical Society of Japan.

PY - 2020/6/8

Y1 - 2020/6/8

N2 - 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,.

AB - 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,.

UR - http://www.scopus.com/inward/record.url?scp=85089135513&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85089135513&partnerID=8YFLogxK

U2 - 10.1093/ptep/ptaa066

DO - 10.1093/ptep/ptaa066

M3 - Article

AN - SCOPUS:85089135513

VL - 2020

JO - Progress of Theoretical and Experimental Physics

JF - Progress of Theoretical and Experimental Physics

SN - 2050-3911

IS - 6

M1 - 063B02

ER -