منابع مشابه
Liouville quantum gravity and KPZ
Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π)−1 ∫ D ∇h(z) · ∇h(z)dz, and a constant 0 ≤ γ < 2. The Liouville quantum gravity measure on D is the weak limit as ε → 0 of the measures ε 2/2eγhε(z)dz, where dz is Lebesgue measure on D and hε(z) denotes the mean value of h on the circle of radius ε centered at z. Given a random (or dete...
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In this paper, we rigorously construct 2d Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov Quantum Geometry of bosonic strings. We also establish some of its fundamental properties like conformal covariance under PSL2(C)-action, Seiberg bounds, KPZ scaling laws, KPZ formula and the Weyl anomaly (Polyakov-Ray-Singer) formula for Liouville Quant...
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In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov. Our approach follows the construction carried out by the authors together with A. Kupiainen in the case of the Riemann sphere. The difference is here that the moduli space for complex tori is non trivial. Modular properties of LQFT are thus investigated....
متن کاملSchramm-Loewner evolution and Liouville quantum gravity.
We show that when two boundary arcs of a Liouville quantum gravity random surface are conformally welded to each other (in a boundary length-preserving way) the resulting interface is a random curve called the Schramm-Loewner evolution. We also develop a theory of quantum fractal measures (consistent with the Knizhnik-Polyakov-Zamolochikov relation) and analyze their evolution under conformal w...
متن کاملLiouville gravity from Einstein gravity
We show that Liouville gravity arises as the limit of pure Einstein gravity in 2+ ε dimensions as ε goes to zero, provided Newton’s constant scales with ε. Our procedure – spherical reduction, dualization, limit, dualizing back – passes several consistency tests: geometric properties, interactions with matter and the Bekenstein-Hawking entropy are as expected from Einstein gravity. Platinum Jub...
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ژورنال
عنوان ژورنال: Nuclear Physics B
سال: 2020
ISSN: 0550-3213
DOI: 10.1016/j.nuclphysb.2019.114913