# Departmental Seminar

## Summation of instantons in O(3) sigma model and quantum-classical duality (mid-term review seminar)

## Audience

**Members of RSPE welcome**

**Mr Boris Runov**

Instantons are special classical solutions of euclidean field equations encountered in gauge theories and sigma models. They describe tunnelling between different topological vacua of quantum field theory. Instantons are essential for understanding non-perturbative low energy behaviour of QFT. In particular, it was conjectured by Polyakov that instantons are responsible for confinement of quarks in QCD. We consider instantons in one of the simplest examples: 2 dimensional O(3) sigma model. Contribution of instantons to partition function of this model can be rewritten in terms of another 2 dimensional integrable QFT known as Lipatov-Boukhvostov model. We study in details its integrable structure and compute vacuum energy of this model using integrability.