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arXiv · 1709.06238

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

Shota Tamura·Hosho Katsura
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Abstract

We study the properties of two-dimensional conformal field theories (CFTs) with sine-square deformation (SSD). We show that there are no eigenstates of finite norm for the Hamiltonian of a unitary CFT with SSD, except for the zero-energy vacuum state $|0\rangle$. We then introduce a regularized version of the SSD Hamiltonian which is related to the undeformed Hamiltonian via a unitary transformation corresponding to the Mobius 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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Shota Tamura, Hosho Katsura. 2017-09-19. Zero-energy states in conformal field theory with sine-square deformation. https://doi.org/10.1093/ptep/ptx147

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