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arXiv · 2208.12169

Unitarity of Symplectic Fermion in $α$-vacua with Negative Central Charge

Shinsei Ryu·Junggi Yoon
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Abstract

We study the two-dimensional free symplectic fermion with anti-periodic boundary condition. This model has negative norm states with 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 negative central charge, $c=-2$, and we clarify how CFT$_2$ with negative central charge can have the non-negative norm. 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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Shinsei Ryu, Junggi Yoon. 2023-02-06. Unitarity of Symplectic Fermion in $α$-vacua with Negative Central Charge. https://doi.org/10.1103/physrevlett.130.241602

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