Liouville quantum gravity on complex tori

@article{David2016LiouvilleQG,
  title={Liouville quantum gravity on complex tori},
  author={Franccois David and R{\'e}mi Rhodes and Vincent Vargas},
  journal={Journal of Mathematical Physics},
  year={2016},
  volume={57},
  pages={022302}
}
In this paper, we construct Liouville Quantum Field Theory (LQFT) on the toroidal topology in the spirit of the 1981 seminal work by Polyakov [Phys. Lett. B 103, 207 (1981)]. Our approach follows the construction carried out by the authors together with Kupiainen in the case of the Riemann sphere [“Liouville quantum gravity on the Riemann sphere,” e-print arXiv:1410.7318]. The difference is here that the moduli space for complex tori is non-trivial. Modular properties of LQFT are thus… 

Liouville quantum gravity on the annulus

  • G. Remy
  • Mathematics
    Journal of Mathematical Physics
  • 2018
In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists

J ul 2 01 8 Liouville quantum gravity on the annulus

In this work we construct Liouville quantum gravity on an annulus in the complex plane. This construction is aimed at providing a rigorous mathematical framework to the work of theoretical physicists

LIOUVILLE QUANTUM GRAVITY AS A METRIC SPACE AND A SCALING LIMIT

  • Jason Miller
  • Mathematics, Physics
    Proceedings of the International Congress of Mathematicians (ICM 2018)
  • 2019
Over the past few decades, two natural random surface models have emerged within physics and mathematics. The first is Liouville quantum gravity, which has its roots in string theory and conformal

Stochastic quantization of Liouville conformal field theory

We study a nonlinear stochastic heat equation forced by a space-time white noise on closed surfaces, with nonlinearity $e^{\beta u}$. This equation corresponds to the stochastic quantization of the

Two Perspectives of the 2D Unit Area Quantum Sphere and Their Equivalence

Abstract2D Liouville quantum gravity (LQG) is used as a toy model for 4D quantum gravity and is the theory of world-sheet in string theory. Recently there has been growing interest in studying LQG in

Probabilistic conformal blocks for Liouville CFT on the torus

Liouville theory is a fundamental example of a conformal field theory (CFT) first introduced by Polyakov in the context of string theory. Conformal blocks are objects underlying the integrable

Introduction to the Liouville quantum gravity metric

Liouville quantum gravity (LQG) is a one-parameter family of models of random fractal surfaces which first appeared in the physics literature in the 1980s. Recent works have constructed a metric

The moduli of annuli in random conformal geometry

. We obtain exact formulae for three basic quantities in random conformal geometry that depend on the modulus of an annulus. The first is for the law of the modulus of the Brownian annulus describing

The Fyodorov–Bouchaud formula and Liouville conformal field theory

  • G. Remy
  • Mathematics
    Duke Mathematical Journal
  • 2020
In a remarkable paper in 2008, Fyodorov and Bouchaud conjectured an exact formula for the density of the total mass of (sub-critical) Gaussian multiplicative chaos (GMC) associated to the Gaussian

Double scaling limits of Dirac ensembles and Liouville quantum gravity

In this paper we study ensembles of finite real spectral triples equipped with a path integral over the space of possible Dirac operators. In the noncommutative geometric setting of spectral triples,
...

References

SHOWING 1-10 OF 37 REFERENCES

Liouville Quantum Gravity on the Riemann Sphere

In this paper, we rigorously construct Liouville Quantum Field Theory on the Riemann sphere introduced in the 1981 seminal work by Polyakov. We establish some of its fundamental properties like

Elliptic functions, Green functions and the mean field equations on tori

We show that the Green functions on flat tori can have either 3 or 5 critical points only. There does not seem to be any direct method to attack this problem. Instead, we have to employ sophisticated

Liouville Field Theory — A decade after the revolution

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory.

Roaming moduli space using dynamical triangulations

SLE and the free field: partition functions and couplings

Schramm-Loewner Evolutions ($\SLE$) are random curves in planar simply connected domains; the massless (Euclidean) free field in such a domain is a random distribution. Both have conformal invariance

Gaussian multiplicative chaos and applications: A review

In this article, we review the theory of Gaussian multiplicative chaos initially introduced by Kahane’s seminal work in 1985. Though this beautiful paper faded from memory until recently, it already

Dimers and analytic torsion I

In the dimer model, a configuration consists of a perfect matching of a fixed graph. If the underlying graph is planar and bipartite, such a configuration is associated to a height function. For

Introduction to Arakelov Theory

Arakelov introduced a component at infinity in arithmetic considerations, thus giving rise to global theorems similar to those of the theory of surfaces, but in an arithmetic context over the ring of

Quantum Geometry of Bosonic Strings