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

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.

37 pages, 9 figures

References in corpus (7)

• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
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• Poking Holes in AdS/CFT: Bulk Fields from Boundary States
• Exact ground state of the sine-square deformed XY spin chain
• Suppression of finite-size effects in one-dimensional correlated systems
• Infinite circumference limit of conformal field theory
• Sine-Square Deformation and its Relevance to String Theory

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