Gerbes, M5-Brane Anomalies and E_8 Gauge Theory

Abstract

Abelian gerbes and twisted bundles describe the topology of the NS-NS 3-form gauge field strength H. We review how they have been usefully applied to study and resolve global anomalies in open string theory. Abelian 2-gerbes and twisted nonabelian gerbes describe the topology of the 4-form field strength G of M-theory. We show that twisted nonabelian gerbes are relevant in the study and resolution of global anomalies of multiple coinciding M5-branes. Global anomalies for one M5-brane have been studied by Witten and by Diaconescu, Freed and Moore. The structure and the differential geometry of twisted nonabelian gerbes (i.e. modules for 2-gerbes) is defined and studied. The nonabelian 2-form gauge potential living on multiple coinciding M5-branes arises as curving (curvature) of twisted nonabelian gerbes. The nonabelian group is in general $\tilde{\Omega }{E}_8$, the central extension of the E_8 loop group. The twist is in general necessary to cancel global anomalies due to the nontriviality of the 11-dimensional 4-form G field strength and due to the possible torsion present in the cycles the M5-branes wrap. Our description of M5-branes global anomalies leads to the D4-branes one upon compactification of M-theory to Type IIA theory.

arXiv comment19 pages

References in corpus (21)

• Eleven-Dimensional Supergravity on a Manifold with Boundary
• D-Branes And K-Theory
• On Flux Quantization In M-Theory And The Effective Action
• E_11 and M Theory
• Five-Brane Effective Action In M-Theory
• Lectures on Special Lagrangian Submanifolds
• Twisted K-theory and K-theory of bundle gerbes
• D-branes, B-fields and twisted K-theory
• WZW branes and gerbes
• Duality Relations Among Topological Effects In String Theory
• Geometry of Deligne cohomology
• Some Relations between Twisted K-theory and E8 Gauge Theory
• Anomalies, Gauss laws, and Page charges in M-theory
• On the formulation of D=11 supergravity and the composite nature of its three-from field
• A Derivation of K-Theory from M-Theory
• Quadratic functions in geometry, topology,and M-theory
• Constructions with bundle gerbes
• The Loop Group of E_8 and K-Theory from 11d
• Twisted K-Theory from Monodromies
• From E_8 to F via T
• Holonomy on D-Branes

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• An Invitation to Higher Gauge Theory
• Twisted differential String and Fivebrane structures
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• Higher Gauge Theory: 2-Connections on 2-Bundles
• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• Categorified Symplectic Geometry and the Classical String
• Noncommutative BTZ Black Hole and Discrete Time
• L-infinity algebra connections and applications to String- and Chern-Simons n-transport
• Fivebrane Structures
• Towards an M5-Brane Model I: A 6d Superconformal Field Theory
• Higher Groupoid Bundles, Higher Spaces, and Self-Dual Tensor Field Equations
• From Loop Space Mechanics to Nonabelian Strings
• Differential cohomotopy versus differential cohomology for M-theory and differential lifts of Postnikov towers
• Note on non-Abelian two-form gauge fields
• Non-Abelian Chiral 2-Form and M5-Branes
• Generalized Kahler geometry and gerbes
• Non-abelian Gerbes and Enhanced Leibniz Algebras
• Non-abelian higher gauge theory and categorical bundle
• The Non-Abelian Self-Dual String and the (2,0)-Theory
• Generalized Yang-Mills Theory and Gravity
• E8 Gauge Theory and Gerbes in String Theory
• Division Algebras, Supersymmetry and Higher Gauge Theory
• Ninebrane structures
• Flux Quantization
• Aspects of Effective Theory for Multiple M5-Branes Compactified On Circle
• Nonabelian 2-forms and loop space connections from SCFT deformations
• Higher Gauge Theory
• Classifying A-field and B-field configurations in the presence of D-branes - Part II: Stacks of D-branes
• Topological Quantum Field Theory on Non-Abelian Gerbes
• Holonomies of Intersecting Branes
• Quasi-quantum groups from Kalb-Ramond fields and magnetic amplitudes for strings on orbifolds
• Non-Geometric Magnetic Flux and Crossed Modules
• Strings with extended non-Abelian gauge interaction
• Flux Quantization on M-Strings