منابع مشابه
Nonperturbative Model of Liouville Gravity
We obtain nonperturbative results in the framework of continuous Liouville theory. In particular, we express the specific heat Z of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres. The integrands are written in terms of the Liouville action. We show that Z satisfies the Painlevé I. Partly supported by the European Community Research Programme Gau...
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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...
متن کاملChiral Liouville Gravity
Classical two-dimensional Liouville gravity is often considered in conformal gauge which has a residual left and right Virasoro symmetry algebra. We consider an alternate, chiral, gauge which has a residual right Virasoro Kac-Moody algebra, and no left Virasoro algebra. The Kac-Moody zero mode is the left-moving energy. Dirac brackets of the constrained Hamiltonian theory are derived, and the r...
متن کاملLiouville 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...
متن کاملNonperturbative Evolution Equation for Quantum Gravity
A scale–dependent effective action for gravity is introduced and an exact nonperturbative evolution equation is derived which governs its renormalization group flow. It is invariant under general coordinate transformations and satisfies modified BRS Ward–Identities. The evolution equation is solved for a simple truncation of the space of actions. In 2+ε dimensions, nonperturbative corrections t...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 1997
ISSN: 0393-0440
DOI: 10.1016/s0393-0440(96)00028-9