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arXiv · 1602.01190

Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories

Nobuyuki Ishibashi·Tsukasa Tada
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Abstract

Elaborating on our previous presentation, where the term {\it dipolar quantization} was introduced, we argue here that adopting $L_0-(L_1+L_{-1})/2+{\bar L}_0-({\bar L}_1+{\bar L}_{-1})/2$ as the Hamiltonian instead of $L_0+{\bar L}_0$ yields an infinite circumference limit in two-dimensional conformal field theory. The new Hamiltonian leads to dipolar quantization instead of radial quantization. As a result, the new theory exhibits a continuous and strongly degenerated spectrum in addition to the Virasoro algebra with a continuous index. Its Hilbert space exhibits a different inner product than that obtained in the original theory. The idiosyncrasy of this particular Hamiltonian is its relation to the so-called sine-square deformation, which is found in the study of a certain class of quantum statistical systems. The appearance of the infinite circumference explains why the vacuum states of sine-square deformed systems are coincident with those of the respective closed-boundary systems.

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Nobuyuki Ishibashi, Tsukasa Tada. 2016-02-03. Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories. https://doi.org/10.1142/s0217751x16501700

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