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2015

Renormalizability of Liouville Quantum Gravity at the Seiberg bound

David, François, Kupiainen, Antti, Rhodes, Rémi et al.

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Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d Riemannian metrics $e^{\phi(z)}dz^2$, conjecturally describing scaling limits of discrete $2d$-random surfaces.

The law of the random field $\phi$ in LQFT depends on weights $\alpha\in \mathbb{R}$ that in classical Riemannian geometry parametrize power law singularities in the metric.
A rigorous construction of LQFT has been carried out in \cite{DKRV} in the case when the weights are below the so called Seiberg bound: $\alpha<Q$ where $Q$ parametrizes the random surface model in question.
These correspond to conical singularities in the classical setup.

Renormalizability of Liouville Quantum Gravity at the Seiberg bound · Around

Built on

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David, F.: Conformal Field Theories Coupled to 2-D Gravity in the Conformal Gauge,
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Knizhnik, V.G., Polyakov, A.M., Zamolodchikov, A.B.: Fractal structure of 2D-quantum gravity,
1988
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Similar

Distler J., Kawai H.: Conformal Field Theory and 2-D Quantum Gravity or Who’s Afraid of Joseph Liouville?,
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Seiberg N.: Notes on Quantum Liouville Theory and Quantum Gravity,
1990
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Troyanov M.: Prescribing curvature on compact surfaces with conical singularities,
Original
1991
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Nakayama Y.: Liouville field theory: a decade after the revolution,
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David F., Kupiainen A., Rhodes R., Vargas V.: Liouville Quantum Gravity on the Riemann sphere,
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Duplantier B., Miller J., Sheffield: Liouville quantum gravity as mating of trees,
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Cited in the paper.

Then

Duplantier B., Rhodes R., Sheffield S., Vargas V.: Critical Gaussian multiplicative chaos: convergence of the derivative martingale,
Original
2014
Later among the works it cites.
Duplantier B., Rhodes R., Sheffield S., Vargas V.: Renormalization of Critical Gaussian Multiplicative Chaos and KPZ formula,
Original
2014
Later among the works it cites.
Rhodes R., Vargas, V.: Gaussian multiplicative chaos and applications: a review, Probab. Surveys vol 11 (2014), 315-392,
Original
2014
Later among the works it cites.

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