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

Tatsuhiro Misumi, Muneto Nitta, Norisuke Sakai

Research output: Contribution to journalArticle

21 Citations (Scopus)

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 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 ${\mathbb C}P{N-{\rm F}-1}$ model, there exist Bogomol' €' nyi-Prasad-Sommerfield (BPS) fractional instantons with topological charges 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 a topological charge greater (less) than one (minus one), that are not decomposable into an instanton-anti-instanton pair and the rest. 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.

Original languageEnglish
Article number033B02
JournalProgress of Theoretical and Experimental Physics
Volume2015
Issue number3
DOIs
Publication statusPublished - 2014 Nov 7

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classifying
instantons
gauge theory
configurations
string theory
unity
boundary conditions
composite materials
matrices

Keywords

  • B23
  • B34
  • B35
  • B37

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes. / Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke.

In: Progress of Theoretical and Experimental Physics, Vol. 2015, No. 3, 033B02, 07.11.2014.

Research output: Contribution to journalArticle

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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 [G. V. Dunne and M. {\"U}nsal, J. High Energy Phys. 1211, 170 (2012); G. V. Dunne and M. {\"U}nsal, 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 ${\mathbb C}P{N-{\rm F}-1}$ model, there exist Bogomol' €' nyi-Prasad-Sommerfield (BPS) fractional instantons with topological charges 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 a topological charge greater (less) than one (minus one), that are not decomposable into an instanton-anti-instanton pair and the rest. 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.",
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