Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes

TL;DR

This paper classifies bion configurations in Grassmann sigma models and related gauge theories using D-brane methods, revealing new types of bions and their properties, which differ from simpler models like ${ m C}P^{N_F-1}$.

Contribution

It introduces a D-brane based classification of bions in Grassmann sigma models, identifying novel BPS fractional instantons and charged bions not present in simpler models.

Findings

Identified all possible bion configurations using D-brane and moduli matrix techniques.

Discovered BPS fractional instantons with topological charge greater than one.

Constructed exact solutions for charged bions in the Grassmann sigma model.

Abstract

We classify bions in the Grassmann $Gr_{N_{\rm F},N_{\rm C}}$ sigma model (including the ${\mathbb C}P^{N_{\rm F}-1}$ model) on ${\mathbb R}^{1}\times S^{1}$ with twisted boundary conditions. We formulate these models as $U(N_{\rm C})$ gauge theories with $N_{\rm F}$ flavors in the fundamental representations. These theories can be promoted to supersymmetric gauge theories and further can be embedded into D-brane configurations in type II superstring theories. We focus on specific configurations composed of multiple fractional instantons, termed neutral bions and charged bions, which are identified as perturbative infrared renormalons by \"{U}nsal and his collaborators. We show that D-brane configurations as well as the moduli matrix offer a very useful tool to classify all possible bion configurations in these models. Contrary to the ${\mathbb C}P^{N_{\rm F}-1}$ model, there exist Bogomol'nyi-Prasad-Sommerfield (BPS) fractional instantons with topological charge greater than unity (of order $N_{\rm C}$) that cannot be reduced to a composite of an instanton and fractional instantons. As a consequence, we find that the Grassmann sigma model admits neutral bions made of BPS and anti-BPS fractional instantons each of which has topological charge greater (less) than one (minus one), that are not decomposable into instanton anti-instanton and the rests. The ${\mathbb C}P^{N_{\rm F}-1}$ model is found to have no charged bions. In contrast, we find that the Grassmann sigma model admits charged bions, for which we construct exact non-BPS solutions of the field equations.