Journal
PHYSICAL REVIEW LETTERS
Volume 116, Issue 13, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.116.130601
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Funding
- Agence Nationale de la Recherche [ANR-10-BLAN-0414: DIME]
- European Research Council (Advanced Grant NuQFT)
- Institut Universitaire de France
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The possibility of extending the Liouville conformal field theory from values of the central charge c >= 25 to c <= 1 has been debated for many years in condensed matter physics as well as in string theory. It was only recently proven that such an extension-involving a real spectrum of critical exponents as well as an analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov formula for three-point couplings-does give rise to a consistent theory. We show in this Letter that this theory can be interpreted in terms of microscopic loop models. We introduce in particular a family of geometrical operators, and, using an efficient algorithm to compute three-point functions from the lattice, we show that their operator algebra corresponds exactly to that of vertex operators V-(alpha) over cap in c <= 1 Liouville theory. We interpret geometrically the limit (alpha) over cap -> 0 of V-(alpha) over cap and explain why it is not the identity operator (despite having conformal weight Delta = 0).
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