Leaving the BPS bound: Tunneling of classically saturated solitons

TL;DR

This paper investigates quantum tunneling between classically BPS saturated solitons in 2D N=2 supersymmetric theories, revealing that instantons mediating tunneling are 1/4 BPS wall junctions, and provides a method to compute tunneling amplitudes via superalgebra charges.

Contribution

It introduces a novel interpretation of soliton tunneling as instantons corresponding to 1/4 BPS wall junctions, and offers a way to calculate tunneling amplitudes using superalgebra charges without explicit solutions.

Findings

Tunneling between BPS states can be described by instantons identified as wall junctions.

Superalgebra central charges enable calculation of instanton actions.

Numerical checks confirm the existence of saturated solutions.

Abstract

We discuss quantum tunneling between classically BPS saturated solitons in two-dimensional theories with N=2 supersymmetry and a compact space dimension. Genuine BPS states form shortened multiplets of dimension two. In the models we consider there are two degenerate shortened multiplets at the classical level, but there is no obstruction to pairing up through quantum tunneling. The tunneling amplitude in the imaginary time is described by instantons. We find that the instanton is nothing but the 1/4 BPS saturated ``wall junction,'' considered previously in the literature in other contexts. Two central charges of the superalgebra allow us to calculate the instanton action without finding the explicit solution (it is checked, though, numerically, that the saturated solution does exist). We present a quantum-mechanical interpretation of the soliton tunneling.