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Conformal Blocks through Integrability and Probability

Project description

Research reveals new insight into 2D conformal field theories

Two-dimensional conformal field theories (2D CFTs) are mathematical models used to describe physical systems that do not change when length, energy or other variables change. Recent research has revealed deep connections between 2D CFTs and other mathematical frameworks. One discovery linked 2D CFT correlation functions to Painlevé equations (a set of non-linear differential equations). Another used probabilistic frameworks such as Gaussian multiplicative chaos (which models randomness) and conformal loop ensembles (which describe random fractal-like curves) to rigorously formulate certain 2D CFTs. With the support of the Marie Skłodowska-Curie Actions programme, the ConBIP project aims to bridge these two approaches using random matrix theory. If successful, ConBIP will uncover universal structures underlying 2D CFTs and resolve critical conjectures in mathematics and physics.

Objective

In the past decade, two major breakthroughs have significantly advanced mathematical physics. The first established a crucial link between the correlation functions of two-dimensional conformal field theories (2D CFTs)—known as conformal blocks—and a special class of integrable systems called the Painlevé equations. This connection, known as the Painlevé/CFT correspondence, led to the derivation of closed-form expressions for the highly transcendental solutions of the Painlevé equations, solving a long-standing problem.

The second breakthrough provided a rigorous formulation of certain 2D CFTs through probabilistic frameworks such as Gaussian Multiplicative Chaos (GMC) measures and Conformal Loop Ensembles (CLE). These concepts have granted unprecedented analytic control over CFTs, particularly in the context of conformal blocks.

This project aims to bridge these two approaches using Random Matrix Theory to develop a unified framework. Achieving this goal is both ambitious and highly desirable, as it would uncover a universal structure underlying CFTs and resolve critical conjectures in both mathematics and physics.

Fields of science (EuroSciVoc)

Keywords

Programme(s)

Topic(s)

Funding Scheme

HORIZON-TMA-MSCA-PF-EF - HORIZON TMA MSCA Postdoctoral Fellowships - European Fellowships

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Call for proposal

(opens in new window) HORIZON-MSCA-2024-PF-01

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Coordinator

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Net EU contribution
€ 276 187,92
Address
WELLINGTON SQUARE UNIVERSITY OFFICES
OX1 2JD Oxford
United Kingdom
Region
South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Activity type
Higher or Secondary Education Establishments
Links
Total cost
No data