QuantGMC · Quantum Field Theory with Gaussian Multiplicative Chaos
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2020-03-09 → 2021-05-08
- EU contribution
- €114,746
- Participants
- 1
- Scheme
- MSCA-IF-EF-ST
Lines connect the coordinator with its partners.
Results in brief
Quantum Field Theory with Gaussian Multiplicative Chaos
The scientific activities of the researcher during the project have given raise to a variety of results in three main directions, -Complex Gaussian Multiplicative Chaos, -Scaling limit for directed polymers and the Stochastic Heat Equation, -Mixing time for effective interface models and particle systems. Complex Gaussian Multiplicative Chaos. The development of Complex Gaussian Multiplicative Chaos theory has been presented as research direction 2 in the DoA. Complex Gaussian Multiplicative Chaos is a random distribution obtained by taking the complex exponential of a Gaussien field whose covariance diverges logarithmically. It is a very natural occurence of a random distribution with fractal properties and has connection with several problems in Theoretical Physics in particular Quantum Field Theory. Scaling limit for directed polymers and the Stochastic Heat Equation In a collaborative effort with Quentin Berger (Université de Paris), we investigated the problem of scaling limit of directed polymer models with an heavy-tailed environment. The directed polymer in a random environment is one of the most studied model for diffusion in a random medium. Mixing time for effective interface models and particle systems. Together with Cyril Labbé (Université Paris Dauphine), Pietro Caputo (Universitá degli Studi Roma Tre) and Shangjie Yang (IMPA - Rio de Janeiro), the researcher also brought new developments on the research concerning the relaxation to equilibrium of physical systems described by a Markov chain. One part of this effort concerns so-called effective interfaces, which are simplified models to account for the time evolution of phase separation in a system. The other is about particle systems in a random environment.
Data: CORDIS, © European Union
Project objective
The proposed goal for our research program is to attack some mathematical problems arising in constructive two dimensional Quantum Field Theory (QFT) and two dimensional Quantum Gravity (QG) using probabilistic methods. The physical theory of Quantum Gravity has the aim of providing a unified framework which encompasses the two descriptions of nature provided by quantum mechanics and general relativity.The two dimensional version of the theory is more tractable than the one corresponding to the four dimensional space-time and thus is used as a testing workbench to understand higher dimensional physics.In order to reinforce the rigourous mathematical understanding of this theory, we wish to explore two particular aspects of QFT which are based on a probabilistic construction called Gaussian Multiplicative chaos. The objectives of QuantGMC are:A- To obtain an explicit construction of canonical random surfaces equipped with a structure of Kähler manifold. In technical terms this corresponds to the construction of a path integral corresponding to the coupling of Liouville functional and the Mabuchi K-energy on 2D manifold of arbitrary genus. B- To enhance the current understanding of the Quantum Sine-Gordon model, which can be interpreted as a random version of the Sine-Gordon equation. This model is conjectured to undergo an infinite sequence of collapse transitions when the inverse temperature increases. However up to now, rigorous renormalization theory of the model can only allow to witness the three first of these transitions. We plan to use Gaussian Multiplicative Chaos to provide a more efficient renormalization scheme which would allow to account for all the transitions.
Original text from CORDIS.
Participants
- UNIVERSITE D'AIX MARSEILLE · MarseilleCoordinatorFrance
Links
Data: CORDIS, © European Union