String Webs from Field Theory

TL;DR

The paper addresses how the spectrum of BPS states in four-dimensional gauge theories with extended supersymmetry changes as one crosses curves of marginal stability on the Coulomb branch, showing that a low-energy ${ m U}(1)^n$ effective action suffices to describe decays even at strong coupling.A semiclassical, boundary-condition–driven construction yields a universal string-web picture in which BPS states are represented by webs on the Coulomb branch, with ends at singular loci and segments following geodesics of the moduli-space metric. The main technical advance is the explicit realization of spike and prong configurations and their projections to string webs for ${ c N}=4$ SU$(N)$ and ${ c N}=2$ theories, unifying brane-based pictures with field-theoretic low-energy dynamics, and clarifying how CMS control the existence and structure of BPS states.These results illuminate the stability and multiplicity of BPS states, connect to D-brane/F-theory constructions, and point to open questions such as the ${s}$-rule for ${ c N}=2$ theories and extensions to other dimensions and gravitational settings.

Abstract

The spectrum of stable electrically and magnetically charged supersymmetric particles can change discontinuously as one changes the vacuum on the Coulomb branch of gauge theories with extended supersymmetry in four dimensions. We show that this decay process can be understood and is well described by semiclassical field configurations purely in terms of the low energy effective action on the Coulomb branch even when it occurs at strong coupling. The resulting picture of the stable supersymmetric spectrum is a generalization of the ``string web'' picture of these states found in string constructions for certain theories.