Renormalizability of Liouville Quantum Gravity at the Seiberg bound

2015/06/05 by David, François, Kupiainen, Antti, Rhodes, Rémi +1
#60D05 #81T20 #81T40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1506.01968

Abstract

Liouville Quantum Field Theory can be seen as a probabilistic theory of 2d Riemannian metrics e^ϕ(z)dz², conjecturally describing scaling limits of discrete 2d-random surfaces. The law of the random field ϕ in LQFT depends on weights α∈ ℝ that in classical Riemannian geometry parametrize power law singularities in the metric. A rigorous construction of LQFT has been carried out in \citeDKRV in the case when the weights are below the so called Seiberg bound: α

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