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

misumi, tatsuhiro; nitta, muneto; sakai, norisuke;

We classify bions in the Grassmann GrNF,NC sigma model (including the CPNF−1 model) on R1 × S1 with twisted boundary conditions. We formulate these models as U  NC  gauge theories with NF 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 Ünsal and his collaborators [G. V. Dunne and M. Ünsal, J. High Energy Phys. 1211, 170 (2012); G. V. Dunne and M. Ünsal, Phys. Rev. D 87, 025015 (2013)]. 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. In contrast to the CPNF−1 model, there exist Bogomol’nyi–Prasad–Sommerfield (BPS) fractional instantons with topological charges greater than unity (of order NC) 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 a topological charge greater (less) than one (minus one), that are not decomposable into an instanton–anti-instanton pair and the rest. The CPNF−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.