Mathematical Physics

Coordinators: Sergey Alexandrov, Vladimir Fateev, Pronob Mitter and André Neveu

There are several topics developed by our team that fit the common umbrella of mathematical physics:

CFT and integrability

Even if the Standard model of particle physics does not possess conformal symmetry, conformal field theories play a special and important role in theoretical physics. They arise as end points of renormalization flows, describe phenomena in condensed matter near critical points and have remarkable physical properties. In two dimensions, CFTs are often integrable, which means that, at least in principle, they can be solved exactly. Our work involves finding such exact solutions, investigation of deformation of the known integrable models and application of the solutions and the integrable model techniques to various physical problems.

Topological invariants and modular forms

String theory and, in particular, its compactifications on Calabi-Yau threefolds provided a fruitful connection with various branches of mathematics such as algebraic geometry, topology and number theory. Remarkably, not only known mathematical results help solving physical problems, but also physics sometimes suggests new ideas and even research directions in mathematics.

Using dualities of string theory and the so-called wall-crossing phenomenon, we obtain new results on topological invariants of Calabi-Yau manifolds. In this research, an important role is played by modular symmetry coming from the famous S-duality. It is worth noting that our work involves not only the standard modular forms, but also mock modular forms and their generalizations that take their origin in the works of Srinivasa Ramanujan.