K-Theory in Quantum Field Theory

Abstract

We survey three different ways in which K-theory in all its forms enters quantum field theory. In Part 1 we give a general argument which relates topological field theory in codimension two with twisted K-theory, and we illustrate with some finite models. Part 2 is a review of pfaffians of Dirac operators, anomalies, and the relationship to differential K-theory. Part 3 is a geometric exposition of Dirac charge quantization, which in superstring theories also involves differential K-theory. Parts 2 and 3 are related by the Green-Schwarz anomaly cancellation mechanism. An appendix, joint with Jerry Jenquin, treats the partition function of Rarita-Schwinger fields.

56 pages, expanded version of lectures at "Current Developments in Mathematics"

References in corpus (6)

• D-Branes And K-Theory
• Tachyon Condensation on the Brane Antibrane System
• Twisted K-theory and K-theory of bundle gerbes
• Higher Algebraic Structures and Quantization
• The Verlinde algebra is twisted equivariant K-theory
• Direct Sum Decompositions and Indecomposable TQFT's

Cited by in corpus (11)

• Setting the quantum integrand of M-theory
• Holographic Action for the Self-Dual Field
• Some Relations between Twisted K-theory and E8 Gauge Theory
• K-Theory from a physical perspective
• Conformal blocks for AdS5 singletons
• Ramond-Ramond fields and twisted differential K-theory
• A New String in Ten Dimensions?
• Anomalous Continuous Translations
• Twisted K-Theory as a BRST Cohomology
• Weak Interaction and Cosmology
• Alphonons as the quanta of the Alfvén waves