# The geometry of the space of BPS vortex-antivortex pairs

**Date**: Wednesday 23 May 2018, 15:00 – 16:00**Location**: Mathematics Level 8, MALL 1, School of Mathematics**Type**: Geometry, Seminars, Pure Mathematics**Cost**: Free

#### Nuno Romao, Institute of Higher Scientific Studies, University of Paris-Saclay. Part of geometry seminar series.

The vortex equations describe BPS configurations in gauged sigma-models on surfaces. Their moduli spaces support Kähler metrics that encode crucial information about the underlying field theories, at both classical and quantum level. An interesting setting is when the target of these field theories is nonlinear -- i.e. a Kähler manifold with holomorphic and Hamiltonian action which does not simply correspond to a group representation.

This setup gives rise to interesting phenomena that are not present in more familiar field theory models that it interpolates, namely, the sigma-model (trivial group) and the gauged linear sigma-model (linear action). Examples of such phenomena are the coexistence of more than one type of solitonic "particle" within the same BPS configuration, and the emergence of boundaries on the moduli spaces that correspond to coalescence of different BPS particles. In my talk, I will report on joint work with Martin Speight, describing very concrete results for the asymptotics of the moduli space metrics, when the target is the 2-sphere with usual circle action.