SO and USp (Hyper)Kahler Quotients and Lumps

TL;DR

This paper constructs explicit Kahler and hyperKahler quotients for SO and USp gauge theories, analyzes their geometric properties, and studies the associated lumps in the non-linear sigma models.

Contribution

It provides explicit metrics for SO and USp hyperKahler quotients and explores the dynamics of lumps within these models.

Findings

Explicit Kahler and hyperKahler metrics derived for SO and USp gauge theories.

Analysis of lump solutions and their effective descriptions.

Insights into the geometric structure of gauge theory moduli spaces.

Abstract

The properties of supersymmetric gauge theories in the Higgs phase at low energies can appropriately be studied by means of a non-linear sigma model, which has the target space being Kahler for N=1 supersymmetric models and hyperKahler for N=2 models. By construction of the Kahler and hyperKahler quotients for the gauge theories with SO and USp gauge symmetries, we obtain the explicit metrics on their respective manifolds. Furthermore, we study the lumps in the non-linear sigma models and their effective description, using the Kahler quotients.