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

Abstract

We classify bions in the Grassmann $G{r}_{N_{\mathrm{F}},N_{\mathrm{C}}}$ sigma model (including the $\mathbb{C}{P}^{N_{\mathrm{F}}-1}$ model) on ${\mathbb{R}}^1\times S^1$ with twisted boundary conditions. We formulate these models as $U(N_{\mathrm{C}})$ gauge theories with $N_{\mathrm{F}}$ 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. 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 $\mathbb{C}{P}^{N_{\mathrm{F}}-1}$ model, there exist Bogomol'nyi-Prasad-Sommerfield (BPS) fractional instantons with topological charge greater than unity (of order $N_{\mathrm{C}}$) 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 $\mathbb{C}{P}^{N_{\mathrm{F}}-1}$ 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.

arXiv comment62 pages, 37 figures

References in corpus (87)

• Brane Dynamics and Gauge Theory
• Vortices, Instantons and Branes
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Solitons in the Higgs phase -- the moduli matrix approach --
• The Moduli Space of N=2 SUSY QCD and Duality in N=1 SUSY QCD
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Resurgence and Trans-series in Quantum Field Theory: The CP(N-1) Model
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Moduli Space of Non-Abelian Vortices
• The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
• All Exact Solutions of a 1/4 Bogomol'nyi-Prasad-Sommerfield Equation
• Multi-Instantons and Exact Results I: Conjectures, WKB Expansions, and Instanton Interactions
• Monopoles in the Higgs Phase
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Uniform WKB, Multi-instantons, and Resurgent Trans-Series
• Instantons in the Higgs Phase
• Continuity, Deconfinement, and (Super) Yang-Mills Theory
• Construction of Non-Abelian Walls and Their Complete Moduli Space
• Generating Non-perturbative Physics from Perturbation Theory
• A semiclassical realization of infrared renormalons
• QCD-like Theories on R_3\times S_1: a Smooth Journey from Small to Large r(S_1) with Double-Trace Deformations
• Continuity and Resurgence: towards a continuum definition of the CP(N-1) model
• Resurgence in QFT: Unitons, Fractons and Renormalons in the Principal Chiral Model
• Non-Abelian Vortices of Higher Winding Numbers
• Resurgence theory, ghost-instantons, and analytic continuation of path integrals
• Semi-superfluid strings in High Density QCD
• Non-Abelian Walls in Supersymmetric Gauge Theories
• Vortices and Other Topological Solitons in Dense Quark Matter
• The Moduli Space of BPS Domain Walls
• Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD
• Localization of Non-Abelian Gauge Fields on Domain Walls at Weak Coupling (D-brane Prototypes)
• Universal Reconnection of Non-Abelian Cosmic Strings
• On the moduli space of semilocal strings and lumps
• Conformality or confinement: (IR)relevance of topological excitations
• Non-Abelian Strings in High Density QCD: Zero Modes and Interactions
• Manifest Supersymmetry for BPS Walls in N=2 Nonlinear Sigma Models
• Multi-Domain Walls in Massive Supersymmetric Sigma-Models
• Domain Walls and Flux Tubes in N=2 SQCD: D-Brane Prototypes
• Non-Abelian Vortices on Cylinder -- Duality between vortices and walls
• Finite size phase transitions in QCD with adjoint fermions
• Instabilities of Non-Abelian Vortices in Dense QCD
• New Phases of SU(3) and SU(4) at Finite Temperature
• 1/2, 1/4 and 1/8 BPS Equations in SUSY Yang-Mills-Higgs Systems -- Field Theoretical Brane Configurations --
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Neutral bions in the $\mathbb{C}{P}^{N-1}$ model
• D-brane Construction for Non-Abelian Walls
• Supersymmetric Nonlinear Sigma Models as Gauge Theories
• Skyrmions from Instantons inside Domain Walls
• Constructing Non-Abelian Vortices with Arbitrary Gauge Groups
• Adjoint QCD on ${\mathbb{R}}^3\times S^1$ with twisted fermionic boundary conditions
• Josephson vortices and the Atiyah-Manton construction
• Webs of Walls
• Instanton constituents in the O(3) model at finite temperature
• Phase diagrams of SU(N) gauge theories with fermions in various representations
• Jewels on a wall ring
• Non-Abelian Webs of Walls
• Microscopic Structure of Magnetic Bions
• Principal Chiral Field at Large N
• Polyakov loops and the Hosotani mechanism on the lattice
• Instanton constituents and fermionic zero modes in twisted CP(n) models
• Global Structure of Moduli Space for BPS Walls
• Domain Walls with Non-Abelian Clouds
• Statistical Mechanics of Vortices from D-branes and T-duality
• Non-Abelian vortices and monopoles in SO(N) theories
• BPS Wall in N=2 SUSY Nonlinear Sigma Model with Eguchi-Hanson Manifold
• Intersecting Solitons, Amoeba and Tropical Geometry
• Vacua of Massive Hyper-Kahler Sigma Models with Non-Abelian Quotient
• Non-Abelian Vortices in SO(N) and USp(N) Gauge Theories
• Dynamics of Domain Wall Networks
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Higgs branch, HyperKahler quotient and duality in SUSY N=2 Yang-Mills theories
• Kinky D-Strings
• Vortices and Monopoles in Mass-deformed SO and USp Gauge Theories
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• D-brane Configurations for Domain Walls and Their Webs
• String Tension Scaling in High-Temperature Confined SU(N) Gauge Theories
• Kinks, chains, and loop groups in the CP^n sigma models
• Phases of Gauge Theories
• A PNJL Model for Adjoint Fermions with Periodic Boundary Conditions
• Phase structure and Hosotani mechanism in gauge theories with compact dimensions revisited
• Nonlinear sigma models at nonzero chemical potential: breaking up instantons and the phase diagram
• Fractionalized Non-Self-Dual Solutions in the CP(N-1) Model
• Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
• Clustering and decomposition for non BPS solutions of the ${\mathbb{CP}}^{N-1}$ models
• Non-integrability of Self-dual Yang-Mills-Higgs System

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• Resurgence of one-point functions in a matrix model for 2D type IIA superstrings
• Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
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• Grassmannian and Flag sigma models on interval: phase structure and L-dependence
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