TY - JOUR
T1 - Unitarity of Symplectic Fermions in α Vacua with Negative Central Charge
AU - Ryu, Shinsei
AU - Yoon, Junggi
N1 - Funding Information:
We thank Changrim Ahn for discussion. S. R. is supported by the National Science Foundation under Grant No. DMR-2001181, and by a Simons Investigator Grant from the Simons Foundation (Grant No. 566116). J. Y. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (Grants No. 2019R1F1A1045971 and No. 2022R1A2C1003182). This research was supported in part by the International Centre for Theoretical Sciences (ICTS) for the program “Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography” (code: ICTS/numstrings-2022/8). J. Y. is supported by an appointment to the JRG Program at the APCTP through the Science and Technology Promotion Fund and Lottery Fund of the Korean Government. This is also supported by the Korean Local Governments—Gyeongsangbuk-do Province and Pohang City. This work is also supported by Korea Institute for Advanced Study (KIAS) grant funded by the Korean Government, and by the Gordon and Betty Moore Foundation through Grant No. GBMF8685 toward the Princeton theory program.
Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.
PY - 2023/6/16
Y1 - 2023/6/16
N2 - We study the two-dimensional free symplectic fermion theory with antiperiodic boundary condition. This model has negative norm states with a naive inner product. This negative norm problem can be cured by introducing a new inner product. We demonstrate that this new inner product follows from the connection between the path integral formalism and the operator formalism. This model has a negative central charge, c=-2, and we clarify how two-dimensional conformal field theory with negative central charge can have a non-negative norm. Furthermore, we introduce α vacua in which the Hamiltonian is seemingly non-Hermitian. In spite of non-Hermiticity, we find that the energy spectrum is real. We also compare a correlation function with respect to the α vacua with that of the de Sitter space.
AB - We study the two-dimensional free symplectic fermion theory with antiperiodic boundary condition. This model has negative norm states with a naive inner product. This negative norm problem can be cured by introducing a new inner product. We demonstrate that this new inner product follows from the connection between the path integral formalism and the operator formalism. This model has a negative central charge, c=-2, and we clarify how two-dimensional conformal field theory with negative central charge can have a non-negative norm. Furthermore, we introduce α vacua in which the Hamiltonian is seemingly non-Hermitian. In spite of non-Hermiticity, we find that the energy spectrum is real. We also compare a correlation function with respect to the α vacua with that of the de Sitter space.
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U2 - 10.1103/PhysRevLett.130.241602
DO - 10.1103/PhysRevLett.130.241602
M3 - Article
C2 - 37390422
AN - SCOPUS:85163621394
SN - 0031-9007
VL - 130
JO - Physical review letters
JF - Physical review letters
IS - 24
M1 - 241602
ER -