Laboratory link : https://www.ipht.fr
Loop models are 2d statistical models which in special cases describe percolation, polymers or random surfaces. This thesis is devoted to exploring the critical limit of loop models. This limit is a family of conformal field theories (CFT), parametrized by the central charge: a complex number whose real part must be less that 13.
The conformal bootstrap method has been used for solving CFTs analytically in two dimensions (minimal models, Liouville theory) or numerically in higher dimensions (the 3d Ising model). Recently, the method has been applied to the 2d O(n) and Potts models: two particuliar classes of loop models. The results are obtained numerically, but they sometimes have simple analytic expressions. Hence the question : can loop models be solved analytically ?
This question will be addressed using a mixture of analytic and numerical techniques :
— Analytic : special functions, representation theory, enumerative geometry.
— Numerical : computing conformal blocks and correlation functions in 2d CFT, simulating loop models on a lattice.
The project may use the following tools : Latex, Git, Python, Jupyter, MediaWiki.
— Introduction to 2d CFT in the bootstrap approach : arXiv :1609.09523.
— Recent results on the 2d O(n) model : arXiv :2111.01106.
In order to fund this PhD project, a possibility is to apply for a scholarship by ED PIF. It is useless to apply without our support, so please get in touch if you are interested. Timetable of ED PIF scholarhips : ED PIF website https://www.edpif.org/
Co-advisors : Jesper Jacobsen (ENS et IPhT), Sylvain Ribault (IPhT)
E-mail : email@example.com , firstname.lastname@example.org
Location : IPhT et/ou ENS