A Rigorous Perspective on Liouville Quantum Gravity & KPZ

Polyakov first understood in 1981 that the summation over random Riemannian metrics involved in transition amplitudes in gauge theory or string theory could be represented mathematically by the now celebrated Liouville theory of quantum gravity. The quantum gravity measure is formally defined by d mugamma = exp[gamma h(z)]dz, where dz is the 2D Euclidean measure; exp[gamma h(z)] is the random conformal factor of the Riemannian metric, with h an instance of the Gaussian free field (GFF) on a bounded domain; and gamma is a constant, 0 2 is also shown to be related to the quantum measure for gamma’ = 4 / gamma.

This is joint work with Scott Sheffield.

Speaker Details

Bertrand Duplantier is the Research Director at the Institut de Physique Théorique, CEA-Saclay, and the former Deputy Director of the Institut Henri Poincaré (Paris). He initiated the Poincaré Seminar, the analogue for Physics of the Bourbaki Seminar. Duplantier studied at Ecole Normale Supérieure (Paris).

Date:
Speakers:
Bertrand Duplantier
Affiliation:
Institute for Theoretical Physics, Saclay-CEA