BPS Saturated Solitons in N=2 Two-Dimensional Theories on RxS (Domain Walls in Theories with Compactified Dimensions)

TL;DR

This paper investigates topologically stable BPS solitons in two-dimensional N=2 supersymmetric theories with compact spatial dimensions, revealing conditions for their existence, classical solutions, and quantum state counting.

Contribution

It provides a complete classification of BPS saturated solitons on a cylinder in N=2 theories, including classical solutions and quantum state enumeration.

Findings

BPS solitons can exist on a compact cylinder contrary to naive expectations

The number of classical BPS solutions depends on the Kahler metric choice

Quantum effects reduce the number of BPS states, which are counted by an auxiliary N=1 quantum mechanics

Abstract

We discuss topologically stable solitons in two-dimensional theories with the extended supersymmetry assuming that the spatial coordinate is compact. This problem arises in the consideration of the domain walls in the popular theories with compactified extra dimensions. Contrary to naive expectations, it is shown that the solitons on the cylinder can be BPS saturated. In the case of one chiral superfield, a complete theory of the BPS saturated solitons is worked out. We describe the classical solutions of the BPS equations. Depending on the choice of the Kahler metric, the number of such solutions can be arbitrarily large. Although the property of the BPS saturation is preserved order by order in perturbation theory, nonperturbative effects eliminate the majority of the classical BPS states upon passing to the quantum level. The number of the quantum BPS states is found. It is shown that the N=2 field theory includes an auxiliary N=1 quantum mechanics, Witten's index of which counts the number of the BPS particles.