Zero-energy states in conformal field theory with sine-square deformation

We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of the finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $\left| {0} \right\rangle$. We then introduce...

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Bibliographic Details
Published inProgress of theoretical and experimental physics Vol. 2017; no. 11
Main Authors Tamura, Shota, Katsura, Hosho
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.11.2017
Subjects
Boundary conditions
Coordinate transformations
Eigenvalues
Energy
Norms
A10
A46
B34
A63
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ISSN2050-3911
2050-3911
DOI10.1093/ptep/ptx147

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Summary:We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of the finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $\left| {0} \right\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Möbius quantization. The unitary equivalence of the two Hamiltonians allows us to obtain zero-energy states of the deformed Hamiltonian in a systematic way. The regularization also provides a way to compute the expectation values of observables in zero-energy states that are not necessarily normalizable.
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptx147