Low-energy dynamics of supersymmetric solitons

Abstract

In bosonic field theories admitting Bogomol'nyi type bounds the low-energy scattering of k solitons can be approximated as geodesic motion on the moduli space of k static solutions. In this paper we consider the analogous issue within the context of supersymmetric field theories. We focus our study on a class of N = 2 non-linear sigma models in d = 2 + 1 based on an arbitrary Kähler target manifold and their associated soliton or “lump” solutions. Using a collective coordinate expansion, we show that the low-energy dynamics of k lumps is governed by an N = 2 supersymmetric quantum mechanics action based on the moduli space of static-charge k-lump solutions of the sigma model. The Hilbert space of states of the effective theory consists of anti-holomorphic forms on the moduli space. The normalisable elements of the dolbeault cohomology classes H (0, p) of the moduli space corresponds to zero-energy bound states and we argue that such states correspond to bound states in the full quantum field theory of the sigma model.