Quantum 1/4 BPS Dyons

TL;DR

This paper constructs explicit quantum 1/4 BPS dyons as bound states of two distinct SU(3) monopoles in the N=4 supersymmetric low-energy moduli-space dynamics. By identifying the correct angular-momentum operator M_a and employing an anti-self-dual ansatz on the Taub-NUT moduli space, the authors derive closed-form bound-state wavefunctions whose spin contents and degeneracies reproduce the expected 1/4 BPS supermultiplets. They show that bound states exist for relative charges |q| ≤ |a|, provide detailed radial forms for the l=q−1, l=q, and l=q−1/2 multiplets (including the special q=0 case), and discuss the behavior near the critical charge and classical limits. The results solidify the connection between low-energy monopole dynamics and the quantum spectrum of 1/4 BPS dyons, with implications for nonperturbative spectra and potential non-BPS bound states and scattering phenomena.

Abstract

Classical properties of 1/4 BPS dyons were previously well understood both in field theory context and in string theory context. Its quantum properties, however, have been more difficult to probe, although the elementary information of the supermultiplet structures is known from a perturbative construction. Recently, a low energy effective theory of monopoles was constructed and argued to contain these dyons as quantum bound states. In this paper, we find these dyonic bound states explicitly in the N=4 supersymmetric low energy effective theory. After identifying the correct angular momentum operators, we motivate an anti-self-dual ansatz for all BPS bound states. The wavefunctions are found explicitly, whose spin contents and degeneracies match exactly the expected results.