Some Relations between Twisted K-theory and E8 Gauge Theory

Abstract

Recently, Diaconescu, Moore and Witten provided a nontrivial link between K-theory and M-theory, by deriving the partition function of the Ramond-Ramond fields of Type IIA string theory from an E8 gauge theory in eleven dimensions. We give some relations between twisted K-theory and M-theory by adapting the method of Diaconescu-Moore-Witten and Moore-Saulina. In particular, we construct the twisted K-theory torus which defines the partition function, and also discuss the problem from the E8 loop group picture, in which the Dixmier-Douady class is the Neveu-Schwarz field. In the process of doing this, we encounter some mathematics that is new to the physics literature. In particular, the eta differential form, which is the generalization of the eta invariant, arises naturally in this context. We conclude with several open problems in mathematics and string theory.

23 pages, latex2e, corrected minor errors and typos in published version

References in corpus (8)

• Twisted K-theory and loop groups
• Quadratic functions in geometry, topology,and M-theory
• Various Faces of Type IIA Supergravity
• T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory
• Twisted K-Theory from Monodromies
• SUSY vs E8 Gauge Theory in 11 Dimensions
• K-Theory in Quantum Field Theory
• IIB Soliton Spectra with All Fluxes Activated

Cited by in corpus (47)

• Nongeometric Flux Compactifications
• Heisenberg Groups and Noncommutative Fluxes
• Twisted differential String and Fivebrane structures
• Anomalies, Gauss laws, and Page charges in M-theory
• Gerbes, M5-Brane Anomalies and E_8 Gauge Theory
• L-infinity algebra connections and applications to String- and Chern-Simons n-transport
• On the formulation of D=11 supergravity and the composite nature of its three-from field
• Fivebrane Structures
• Rational sphere valued supercocycles in M-theory and type IIA string theory
• Type IIB String Theory, S-Duality, and Generalized Cohomology
• Framed M-branes, corners, and topological invariants
• The Rational Higher Structure of M-theory
• Type II string theory and modularity
• Duality symmetry and the form fields of M-theory
• Gauge enhancement of super M-branes via parametrized stable homotopy theory
• Flux Quantization and the M-Theoretic Characters
• Geometry of Spin and Spin^c structures in the M-theory partition function
• Type II Actions from 11-Dimensional Chern-Simons Theories
• M-theory and Characteristic Classes
• Twisted Cohomotopy implies M5-brane anomaly cancellation
• Real ADE-equivariant (co)homotopy and Super M-branes
• The Elliptic curves in gauge theory, string theory, and cohomology
• The character map in (twisted differential) non-abelian cohomology
• Ramond-Ramond fields and twisted differential K-theory
• A Higher Twist in String Theory
• Duality and cohomology in M-theory with boundary
• Massey products in differential cohomology via stacks
• M-Theory with Framed Corners and Tertiary Index Invariants
• E8 Gauge Theory and Gerbes in String Theory
• Flux Quantization
• Loop Groups, Kaluza-Klein Reduction and M-Theory
• The Loop Group of E8 and Targets for Spacetime
• M-theory, the signature theorem, and geometric invariants
• On the geometry of the supermultiplet in M-theory
• Higher Structures in M-Theory
• Superbranes, D=11 CJS supergravity and enlarged superspace coordinates/fields correspondence
• Flux Quantization on Phase Space
• Corners in M-theory
• Topics on D-brane charges with B-fields
• Cyclification of Orbifolds
• Topological aspects of the NS5-brane
• T-duality in rational homotopy theory via $L_{\infty }$-algebras
• The Hidden M-Group
• Gravitational monopoles, anomalies and M$E_8$ bundles
• M Theory, Type IIA Superstrings, and Elliptic Cohomology
• Flux Compactifications on Projective Spaces and The S-Duality Puzzle
• OP2 bundles in M-theory